This post is one in a series on the book How to Think about Weird Things: Critical Thinking for a New Age by Theodore Shick, Jr. and Lewis Vaughn. (Fifth Edition)
Unless noted otherwise all quotes used in this series are from that book, usually with the page number noted in parenthesis.
The series should be read in order starting with the first post.
"Arguments, Good, Bad, and Weird
The central focus of critical thinking is formulation and evaluation of arguments - and this is true whether the subject matter is ordinary or as weird as can be. Usually when we are doing critical thinking, we are trying either to devise arguments or to assess them. We are trying either (1) to demonstrate that a claim, or proposition, is true or (2) to determine whether in fact a claim is true. In either case, if we are successful, we are likely to increase our knowledge and expand our understanding - which is, after all, the main reason we use critical thinking in the first place." (Page 35)
"As noted earlier, we are entitled to believe a claim when we have good reasons to believe it. The reasons for accepting A claim are themselves stated as claims. The combination of claims - a claim (or claims) supposedly giving reasons for accepting another claim is known as an argument. Or to put it another way, when claims (reasons) provide support for another claim, we have an argument.
People sometimes use the word argument to refer to a quarrel or verbal fight. But this meaning has little to do with critical thinking. In critical thinking, an argument is defined as above - reasons supporting a claim.
To be more precise, claims (or reasons) intended to support another claim are known as premises. The claim that the premises are intended to support is known as the conclusion." (Page 36)
"There are also different kinds of arguments. Arguments can be either deductive or inductive. Deductive arguments are intended to provide conclusive support for their conclusions. Inductive arguments are intended to provide probable support for their conclusions. A deductive argument that succeeds in providing conclusive support is said to be valid. A deductive argument that fails to provide such support is said to be invalid. A valid deductive argument has this characteristic: If its premises are true, its conclusion must be true. In other words, it is impossible for a deductively valid argument to have true premises and a false conclusion. Notice that the term valid as used here is not a synonym for true. Valid refers to a deductive argument's logical - it refers to to an argument structure that guarantees the truth of the conclusion if the premises are true. If an argument is valid, we say that the conclusion follows from the premises. Because a deductively valid argument guarantees the truth of the conclusion if the premises are true, it is said to be truth-preserving.
Here's a classic deductively valid argument:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
And here's another one:
If you have scars on your body, then you have been abducted by space aliens. You obviously do have scars on your body. Therefore, you have been abducted by space aliens.
Notice that in each of these, if the premises are true, the conclusion must be true. If the premises are true, the conclusion cannot possibly be false. This would be the case regardless of the order of the premises and regardless of whether the conclusion came first or last.
Now here are deductively invalid versions of these arguments:
If Socrates is a dog, he is mortal.
Socrates is not a dog.
Therefore, Socrates is not mortal.
If you have scars on your body, then you have been abducted by space aliens. You have been abducted by space aliens. Therefore, you have scars on your body.
These arguments are invalid. In each, the conclusion does not follow from the premises." (Page 39-40)
"An inductive argument that succeeds in giving probable support to its conclusion is said to be strong. An inductive argument that fails to do this is said to be weak. In an inductively strong argument, if the premises are true, the conclusion is probably or likely to be true. The logical structure structure of an inductively strong argument can only render the conclusion probably true if the premises are true. Unlike a deductively valid argument, an inductively strong argument cannot guarantee the truth of the conclusion if the premises are true. So inductive arguments are not truth-preserving.
Here are two inductively strong arguments:
If Socrates is a man, he is most likely mortal.
He is a man.
Therefore, Socrates is probably mortal.
If you have scars on your body, there is a 90 percent chance that you have been abducted by space aliens. You have scars on your body. So you have probably been abducted by space aliens.
Look at the first inductive argument. Notice that it's possible for the premises to be true and the conclusion false. After all, the first premise says that there is no guarantee that Socrates is mortal just because he's a man. He's only likely to be mortal. Also, in the second argument, there is no guarantee that you have been abducted by space aliens if you have scars on your body. If you have scars on your body, there's still a 10 percent chance that you have not been abducted.
Good arguments must be valid or strong - but they also must have true premises. A good argument is one that has the proper logical structure and true premises. Consider this argument:
All dogs can lay eggs.
The prime minister is a dog.
Therefore, the prime minister can lay eggs.
This is a valid argument, but the premises are false. The conclusion follows logically from the premises - even though the premises are false. So the argument is not a good one. A deductively valid argument with true premises is said to be sound. A sound argument is a good argument. A good argument gives you good reasons for accepting the conclusion. Likewise, A good inductive argument must be logically strong and have true premises. An inductively strong argument with true premises is said to be cogent. A cogent argument is a good argument, which provides good reasons for accepting the conclusion. " (Page 40-41)
"DEDUCTIVE ARGUMENTS
Whether a deductive argument is valid depends on its form or structure. We can see the form most easily if we represent it by using letters to substitute for the argument's statements. Consider this deductive argument:
1. If the soul is immortal, then thinking doesn't depend on brain activity.
2. The soul is immortal.
3. Therefore, thinking doesn't depend on brain activity.
By using letters to represent each statement, we can symbolize the argument like this:
If p then q.
p.
Therefore, q.
The first line is a compound statement consisting of two constituent statements, each of which is assigned A letter: p or q. Such a compound statement is known as a conditional, or if-then, statement. The statement following the if is called the antecedent, and the statement after then is called the consequence. The whole argument is referred to as a conditional argument because it contains at least one conditional statement (If p then q.)
Conditional arguments are common. In fact, many conditional argument patterns are so common that they have been given names. These prevalent forms are worth getting to know because they can help you quickly judge the validity of arguments you encounter. Since the validity of an argument depends on its form, if you know that a particular common form is always valid (or invalid), then you know that any argument having that same form must also be valid (or invalid).
For example, the argument just examined is cast in the common form known as affirming the antecedent, or modus ponens. Any argument in this form is always valid. We may drop whatever statements we please into this form, and the argument will remain unshakably valid - whether or not the premises are true. Now consider this modus ponens argument:
1. If one human is made of tin, then every human is made of tin.
2. One human is made of tin.
3. Therefore, every human is made of tin.
The premises and conclusion of this argument are false. Nevertheless, this argument is valid because if the premises were true, then the conclusion would have to be true. A valid argument can have false premises and a false conclusion, false premises and a true conclusion, or true premises and a true conclusion. The one thing it cannot have is true premises and a false conclusion.
Here is another frequently occurring, conditional form:
If p then q.
Not q.
Therefore, not p.
For example:
1. If the soul is immortal, then thinking doesn't depend on brain activity.
2. Thinking does depend on brain activity.
3. Therefore, the soul is not immortal.
This form is known as denying the consequen, or modus tollens. Any argument patterned this way - regardless of the topic or truth of the premises - is valid.
A valid hypothetical form that people often employ to think critically about a series of events is known as hypothetical syllogism. (Hypothetical is a synonym for conditional, A syllogism is simply a deductive argument consisting of two premises and a conclusion.) In this form, every statement is conditional. See:
If p then q.
If q then r.
Therefore, if p then r.
For example:
1. If the floor creaks, someone is standing in the hallway.
2. If someone is standing in the hallway, there's a burglar in the house.
3. Therefore, if the floor creaks, there's a burglar in the house.
As you might expect, some very common argument forms are invalid. This is known as denying the antecedent:
If p then q.
Not p.
Therefore, not q.
1. If Joe is a bachelor, then Joe is a male.
2. Joe is not a bachelor.
3. Therefore, Joe is not a male.
The invalidity of the argument seems obvious. But consider this specimen in the same form:
1. If scientists can prove the existence of ghosts, then ghosts are real.
2. But scientists cannot prove the existence of ghosts.
3. Therefore, ghosts are real.
The dead giveaway of invalidity here is that it's possible for both premises to be true and the conclusion false. Even if scientists cannot prove the existence of ghosts, that doesn't show that ghosts are not real. Perhaps ghosts exist despite the failure of science to prove it.
Another popular invalid form is affirming the consequent:
If p then q.
q.
Therefore, p.
1. If Chicago is the capital of Illinois, then Chicago is in Illinois.
2. Chicago is in Illinois.
3. There, Chicago is the capital of Illinois.
We can see immediately that this argument is invalid because, you will recall, it's impossible for a valid argument to have true premises and a false conclusion - and this argument clearly does have true premises and a false conclusion.
Of course, not all common deductive arguments are conditional. Here's a nonconditional valid form known as distinctive syllogism:
Either p or q.
Not p.
Therefore, q.
1.Either Jill faked the UFO landing or Jack did.
2. Jill did not fake the UFO landing.
3. Therefore, Jack faked the UFO landing.
A statement in the p-or-q format of premise 1 is called a disjunction, and each statement in a disjunction (p or q) is called a disjunct. In a disjunctive syllogism, either one of the disjuncts can be denied, and the conclusion is that the undenied disjunct must be true.
Being familiar with these six argument forms can come in handy when you're trying to quickly determine the validity of an argument." (Page 41-43)
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