Avoiding Fallacious Reasoning: Lesson 4

Premises and Conclusions

A statement, or claim, is an assertion that something is or is not the case. It is the kind of utterance that is either true or false. These are statements:

A tree is growing in the quad.

I am shocked and dismayed.

2+2=4

Statements are further broken down into premises and conclusions, as mentioned in lesson 1.

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“An argument is a combination of statements in which some of them are intended to support another of them” (42).

Translate this: ”Combination of statements in which some of the statements are intended to provide reasons for believing another statement is true” (22).
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Inductive argument

“An argument meant to offer probable support for its conclusion. Inductive arguments can be strong or weak. A strong argument with true premises is said to be cogent.

enumerative induction

“We arrive at a generalization about an entire group of things after observing just some members of the group” (33).

If the number of the group of things is not adequate, then it becomes our old friend fallacy, the hasty generalization. A weak enumerative induction argument is the same as hasty generalization.

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Translate this: ”Every formatted disk I have bought from the computer store is defective. Therefore, all formatted disks sold at the computer store are probably defective(assume that the sample is large enough)”(33). Use strong or weak
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“Based on what we know about this sample, can we generalize to all the members”(34)?

This is the key question to determine whether it’s a hasty generalization(weak enumerative induction) or strong enumerative induction.

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“If the sample is sufficiently large and representative…the argument is strong” (34).

“If the sample is inadequate then the argument is weak”(34).

analogical induction

“Two or more things are similar in several ways; therefore, they are probably similar in one further way”(35).

“The form of analogical induction:

X has properties P1,P2,P3 plus the property P4

Y has properties P1, P2, and P3

Therefore, Y probably has property P4”(35).

Strong: relevant similarities

Weak: irrelevant similarities

Determine whether these analogical induction arguments are weak or strong:

Translate this: “Humans can walk upright, use simple tools, learn new skills, and devise deductive arguments. Chimpanzees can walk upright, use simple tools, and learn new skills. Therefore, chimpanzees can probably devise deductive arguments
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“There are unmentioned dissimilarities. The brain of a chimpanzee is smaller and more primitive than that of a human, a difference that probably inhibits higher intellectual functions such as logical argument”(36).

Translate this: ”A watch is a complex mechanism with many parts that seem arranged to achieve a specific purpose – a purpose chosen by the watch’s designer. In a similar fashion, the universe is a complex mechanism with many parts that seem arranged to achieve a specific purpose. Therefore, the universe must also have a designer”(35).
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“Although the universe resembles a watch in some ways, in other ways it does not resemble a watch. Specifically, the universe also resembles a living thing”(36).

Inference to the best explanation is also known as abduction

“Recall that an argument gives us reasons for believing that something is the case. An explanation, on the other hand, states how or why something is the case. It attempts to clarify or elucidate, not offer proof” (36).

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The typical form of inference to the best explanation:

Phenomenon Q

E provides the best explanation for Q

Therefore, it is probable that E is true.

Deductive arguments

“Deductive arguments are supposed to offer logically conclusive support for their conclusions. If a deductive argument actually manages to provide logically conclusive support for its conclusion, it is said to be valid. If it fails to provide logically conclusive support for the conclusion, it is said to be invalid”(28).

Determine whether the following argument is valid or invalid.

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Notice that valid is not a synonym for true. A valid arguments is simply a conclusion following from its premises.

“All soldiers are brave” is a false premise, but the argument is logically valid.

Translate this: ”If stealing harms people, then it is morally wrong. Stealing does harm people. Therefore, stealing is morally wrong”(28). Valid or invalid?
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Both of these arguments are symbolized like this:

If p, then q.

p.

Therefore, q.

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Classify the following arguments:

Translate this: ”Almost all of the students at this school are Democrats. Therefore, Maria, who is a student here, is probably a Democrat too”(29).
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Translate this: ”Ninety percent of the Republicans I know are Volvo owners. Therefore, 90 percent of all Republicans are probably Volvo owners”(29). Use weak or strong
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Determine whether the conclusion follows from the premises

“Usually, the first step in assessing the worth of an argument is to determine whether the conclusion follows form the premises – that is, whether the argument is valid or strong. If the conclusion does not follow from the premises, then the argument cannot give you good reasons to accept the conclusion. The argument is bad – even if the premises are true”(30).

3 basic deductive patterns of the conditional form

Deductive arguments occur in patterns, and the 3 basic conditional patterns will be covered.

“If stealing harms people, then it is morally wrong. Stealing does harm people. Therefore, stealing is morally wrong”(30).

If p, then q.

p.

Therefore, q.

This pattern is the conditional form. The if premise is the antecedent. The then premise is the consequent.

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This type of condition is known as affirming the antecedent

The Latin for affirming the antecedent is modus ponens

Now on to the next conditional deductive argument.

“If the cat is on the mat, then she is asleep. If she is asleep, then she is dreaming. Therefore, if the cat is on the mat, then she is dreaming”(32).

If p, then q.

If q, then r.

Therefore, if p, then r.

This form is know as the hypothetical syllogism

As for the last type, it’s the denying the consequent, known in Latin as modus tollens.

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Modus tollens is as follows:

If p, then q.

Not q.

Therefore, not p.

“If the mind is identical to the brain, then damaging the brain will damage the mind. But damaging the brain will not damage the mind. Therefore, the mind is not identical to the brain”(31).

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Invalid Conditional Argument Forms

Denying the antecedent and affirming the consequent are two types of invalid conditional forms that can easily be detected. While one can use a substitution method to determine invalidity(true premises and false conclusion), it’s easier to just memorize these two types of invalid conditional forms, especially on time restricted exams..

If p, then q

Not p.

Therefore, not q.

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If p, then q.

q

Therefore, p

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Translate this: If Polaris is a star, then I’m a winner. Polaris is not a star. Therefore, I’m not a winner. Determine which of the 5 conditional forms this argument takes. Then, determine if it’s valid.
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This argument takes the form:

If P, then W

not P

Therefore, not W

This was all I relevant study material I was able to collect from Vaughn’s chapters regarding logic

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