Lesson 2 General Rules of Thumb

What can “few” also be diagrammed as?

“Some.” Few can also be diagrammed as “most are not” X—→ most /Y

Can you ever put two somes together?

NO

What is the relationship between “many” and “some” in terms of how they imply each other?

“Many” can imply “some” but NEVER the other way around. In logical arguments, "many" suggests a quantity greater than one, thereby indicating that at least "some" are included.

What kind of arrow do “if and only if” statements have?

a double arrow. This implies that both variables will either exist or not exist at the same time

Can you ever put a “most” statement after an “all” when the sufficient is the bridge variable in common?

NO. A most following an all is a bad argument in this case

What requirements do you need for a good argument when dealing with conditional statements? Which argument template is the exception to this rule?

A good argument MUST have:

1. A conditional statement (like X—→ Y)

2. The Bridge variable in common must be the SUFFICIENT condition (X) in common

Argument template #12 is the exception to this rule (it has a double “most,” but since both “mosts” come off the same variable A it is OK):

P: A—(most)—> B

P: A—(most)—> C

C: BsomeC

When you put a “some” in front of an “all” statement, with the sufficient being the bridge variable in common, is this a good or a bad argument?

GOOD argument

When you put an “all” statement in front of a “some,” with the bridge variable being the sufficient, is this a GOOD or BAD argument?

BAD argument. You can never have a some statement following an absolute.

“Some…not” is the same thing as?

“Not all”

Can you turn a most into a some statement?

Yes! But never the other way around!

what is the logical opposite of must be true?

could be false/not necessarily true

what is the logical opposite of must be false?

could be true/not necessarily false

what is the logical opposite of could be true?

must be false/cannot be true

logical opposite of could be false

must be true/cannot be false

logical equivalent of must be true

cannot be false!

logical equivalent of must be false?

cannot be true!

logical equivalent of could be true?

not necessarily false

logical equivalent of could be false

not necessarily true

logical equivalent of not necessarily true?

could be false

logical equivalent of not necessarily false

could be true

are “some…not” statements reversible?

NO. Saying “Some fruits are not apples” does not equal the statement “some apples are not fruits”