1. How to Think Logically

2. From Unclear Language to Unclear Reasoning

3. Causes of Linguistic Unclarity
Vagueness: When a word is vague to a significant degree, its reference is unclear. When a statement is vague to a significant degree, it is neither determinately true nor determinately false.
Ambiguity: When an expression is ambiguous, it has more than one meaning, and it is unclear which meaning is intended by the speaker.
Confused predication

4. Fallacies of Unclear Language

5. Semantic Unclarity
Vagueness and ambiguity are forms of semantic unclarity that may affect linguistic expressions of different kinds, as well as the logical relations between them.
When an expression is vague, it is unclear whether or not certain cases fall within its reference.
When an expression is ambiguous, it is unclear which of its possible meanings is the one intended by the speaker.

6. Vagueness and Indeterminacy
When either the premise or conclusion of an argument is significantly vague, that statement is indeterminate; neither determinately true nor determinately false.
Such indeterminacy undermines the argument as a whole.

7. Summary of Vagueness When a term is vague:
It is indeterminate whether it applies or not to certain borderline cases.
There is no cutoff between the cases to which it determinately applies and those to which it determinately does not.
When a statement is vague, it is neither determinately true nor determinately false.

8. What’s Wrong With This Argument?

9. Definition of Paradox
A paradox is a puzzle without apparent solution involving claims that cannot all be true at once, even though each seems independently true.
Standardly, a paradox may be dealt with in one of two ways: it may be solved or it may be dissolved.
To solve a paradox, at least one of its claims must be shown false.
To dissolve it, it has to be shown that the claims are not really inconsistent.

10. The Heap Paradox
An argument that trades on the vagueness of some term so that, although it appears a valid inference from premises that are seemingly true, it draws a conclusion that is plainly false. The argument creates a paradox or puzzle—which is a problem without obvious solution.

11. The Heap Paradox

12. Slippery Slope Fallacy
A slippery-slope argument proceeds from a premise about a harmless scenario to one or more premises about apparently similar scenarios that are taken to have unwelcome consequences, either flouting well-accepted rules or leading to disaster.
The argument would commit a fallacy just in case there is no good reason to think:
that the scenarios in question are analogous in the way assumed in the argument
that the chain of events envisioned will in fact happen as assumed in the argument

13. How to Avoid the Slippery Slope Fallacy
Reject the principle fueling a slippery-slope argument; if something is true in some given case, it doesn’t guarantee that it’s true in any other similar case.
Although it is reasonable that similar cases share many predicates, small differences in a series of cases can add up to a big difference between the initial case and the one featured in the slippery-slope argument’s conclusion. The slippery-slope arguer fails to take this into account.

14. Ambiguity
Vagueness must be distinguished from ambiguity. A word or phrase is vague if its reference is indeterminate.
But a word is ambiguous if it has more than one meaning, and a given context makes it unclear which meaning is intended.
When an ambiguous word occurs in an argument’s premise, it may be uncertain whether the argument’s conclusion is supported by it at all.

15. Equivocation
Equivocation occurs when some crucial expression is used with more than one meaning over the course of an argument.
For example, in one place a word means one thing, in another something else—and the argument appears to support the conclusion only as long as one doesn’t notice that there has been this shift in meaning. For example:
1. All laws require a lawmaker.
2. Galileo’s principle of inertia is a law.
3. Galileo’s principle of inertia requires a lawmaker.

16. How to Avoid Equivocation
In evaluating an argument, check thoroughly to be sure that its crucial expressions:
Have unambiguous meaning.
Have the same meaning in each occurrence in the argument.

17. Amphiboly
In amphiboly, it’s the awkward construction of sentences—the confusing way their words are arranged—that renders them unclear, and so invites drawing the wrong conclusion from them. For example:
1. Your arm hurts in two places.
2. Pain is to be avoided.
3. You shouldn’t go to those places where your arm hurts.

18. How to Avoid Amphiboly
When evaluating an argument, be alert for ambiguous word order in the premises that leaves uncertain whether they do in fact support the argument’s conclusion.

19. Confusion in Predication
Confusion in predication leads to defects in reasoning that happen when the arguer fails to notice either of these:
Some properties that apply to a whole, a class of things, or a collective group, as stated in an argument’s premises, do not apply to each part of the whole or to each individual member of the class or group as stated in its conclusion.
Conversely, some properties that apply to a part of a whole, or an individual member of a class or a group as stated in an argument’s premises, do not apply to the entire whole, class, or group as stated in its conclusion.

20. Composition Confused predication underlies the fallacy of composition.
Composition rests on the mistake of thinking that, since each of the parts of some whole, or each of the members of a class or group, has a certain property, therefore the whole, class, or group itself also has that same property. For example:
1. Each player for the Chicago Cubs is an excellent player.
2. The Chicago Cubs are an excellent team.

21. How to Avoid the Fallacy of Composition
It is one thing to predicate a property of each individual member of a team, class, and so on, but quite another to predicate it of the team itself. What may be true in the one case might not be so in the other.
If an argument concludes that a whole itself has a certain property on the basis of its parts each having that property individually, it commits the fallacy of composition and should be rejected.

22. Division Another fallacy of confused predication is division.
Division rests on the mistake of thinking that because the whole has a certain property, therefore each of the parts or members that make it up has that same property. For example:
1. The U.S. Congress represents every state in the Union.
2. Each member of the U.S. Congress represents every state in the Union.

23. How to Avoid the Fallacy of Division
In evaluating an argument, ask whether it concludes that each part of a whole has a certain property on the basis of the whole having that property.
If it does, the argument commits the fallacy of division and should be rejected.

24. Summary of Confused Predication
In evaluating an argument, check whether:
It concludes that each part of a whole has a certain property because the whole has that property.
It concludes that a whole itself has a certain property because each of its parts has that property individually.
If either of these is the case, then the argument commits one of the fallacies of confused predication and must therefore be rejected.