Logos

Logos, in Latin literally meaning "word," is the thing that is said, the claim, the thesis, the whole argument. Arguments exist around thesis, therefore arguments exist around logos.

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)

Logical Appeal

Reached according to a pattern of testable correct (valid) inference.

Valid

Follows a logical pattern of testable correct inference

True

verifiable; actually the case

VALID + TRUE = SOUND

Categorical Syllogism

All men are mortal (major premise)
Socrates is a man (minor premise)
Socrates is mortal (conclusion)

  • Premise = means by which you reach your conclusion and build your argument
  • Major Premise = incontrovertible, universally agreed upon
  • Minor Premise = inestablished fact, related to topic
  • Conclusion = subject of conclusion (minor term) -> middle term -> predicate of conclusion (major term)

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 term, S is the minor term, and M is the term that links both major and minor terms)

When combined with the 4 types of 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

When narrowed down by the rules of formal fallacy, 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.

Toulmin Model

Claim (Conclusion) = I should wear a coat
- because -
Data (Minor Premise) = its cold outside
- and -
Warrant (Major Premise) = coats make you warm
- due to -
Backing = they are thick and insulated
Qualifier = unless
Rebuttal = it has a big hole in it

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