Logos

Logos is the logical portion of the Rhetorical Appeals, which refers to the clarity of the speaker's claim and the effectiveness of the supporting evidence.

Sections

Basic logical arguments are structured into three consecutive parts: the major premise, minor premise, and conclusion.

Major Premise

The major premise is an incontrovertible claim and is normally a general statement about the function of the world. (e.g. all dogs are mammals) For an argument to be valid, it must have a major premise that is undeniable.

Minor Premise

The minor premise of an argument is a specific fact that leads to the conclusion. (Gary is a dog) In an argument, it usually takes the form of data or an observation and is almost always stated in the argument.

Conclusion

The conclusion is information drawn from both premises (Because Gary is a dog, we know he is a mammal) and is normally what an argument is focused on proving. If the argument is logically constructed, then the conclusion created by it is logical. (it follows a pattern of testably correct inference)

Making a Logical Argument

Statements

A statement in a logical argument can be divided into 4 separate categories:

  • A: All S are P
  • I: Some S are P
  • O: Some S are not P
  • E: All S are not P

Figures

There are also four different structures that an argument can take:
Figure 1:
M-P
S-M
S-P
Figure 2:
P-M
S-M
S-P
Figure 3:
M-P
M-S
S-P
Figure 4:
P-M
M-S
S-P
(Where P is the major premise, S is the minor premise, and M is the term that links both major and minor premises)

When combined with the 4 statements, this creates 256 different forms of syllogism. For example, an EIO-3 syllogism states that no M's are P's and some M's are S's. It follows that some S's are not M's. If you wanted to substitute factual statements to check the if the argument is constructed logically, you may come up with a statement like this:
No cats are communists.
Some cats are pets.
Some pets are not communists.

This is a valid form of an argument. (it is also true unless cat communists actually exist, which is possible but not scientifically proven as of right now)

Valid Argumentative Structures

There are 16 valid structures an argument can take, which can be remembered using Mr. Johnson's poem:
1. Adamant teacher maligning Hesiod
2. Teacher alleges Hesiod aloof
3. Hesiod's orator: "maligning villain!"
4. Alleges villain Hesiod.

The vowels in this poem represent the statements that lead to a logical argument, while the lines of the poem refer to which structure those statements will be logical in. For example, the word "orator" in the poem corresponds to the OAO-3 syllogism, because it contains the vowels O, A, and O (in that order) and is found on line three of the poem.
Note: If you choose to memorize this poem, make sure you know how to spell the words found in it. It would be very sad if you were to get a question wrong on the AP test because you thought that orator was spelled "orater" and stated that the OAE-3 syllogism is valid.

Errors

Below are formal fallacies that relate directly to the organization or an argument. Informal Fallacies are errors in interpretation of data, improper patterns of thinking, and other errors unrelated to the actual structure of an argument.

The Fallacy of Four Terms

A logical argument can never contain more than three terms. For example:

All black and white things are explicit.
All penguins are black and white.
All penguins are explicit.

This syllogism is structurally valid because it follows the AAA-1 pattern, but the logic of this statement falls apart due to the double meaning of "black and white" is taken into account. (it can mean that something is clearly defined, or it can mean the combination of the colors black and white) Because "black and white" actually has two different meanings, the middle term doesn't actually connect both premises and the syllogism falls apart. Any syllogism is invalid if it involves four or more terms, even if it doesn't contain homographs. These are normally easier to spot because they are completely nonsensical most of the time. (All sandwiches are delicious, and all hoagies are sandwiches. Therefore, hoagies help you live longer.)

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