PHIL 210: Exam 1 (Syllogisms)

Valid

The conclusion follows from premises

Sound

Valid + all premises are true

Soundness

An argument is sound if its valid and every premise is true

Statements are ____ or _____ and arguments are ____ or ____

True/False; Valid/Invalid

What is the distribution test?

A letter is distributed in a wff if it occurs just after all or any where after no or not

Star Test

Star distributed letters in premise and undistributed ones in conclusion

Star Validity

Syllogism is only valid if every capital letter is starred exactly once and there is exactly one star on the right-hand side

Every/each/any/whoever = ____

All

A’s are B’s = _________

All A is B

Only men are NFL football players can be translated into what?

All F is M

No one is an NFL player unless they are a man can be translated into what?

All F is M

If both conclusion letters are capital:

Use an “all” or “no” if every premise starts with all or no; otherwise use some

If at least one letter in the conclusion is small:

The conclusion will have a small letter is/is not and then a letter

Always derive a _____ conclusion if any premise has no or not

Negative

All, all = ___

All

All, no = ____

No

All, some = _____

Some

All, some is not = ______

Some is not

No, some = _____

Some is not

x is A, x is B = _____

Some A is B

All or no premises in venn diagrams should be ____

Shaded

Some premises in venn diagrams should be ____

X

Venn Diagrams: No A is B

Shade where A and B overlap

Venn Diagrams: All A is B

Shade where A and B do not overlap

Venn Diagrams: Some A is B

Put a X where A overlaps B

Venn Diagrams: Some A is not B

Put a X where A does not overlap B

How to solve idiomatic arguments:

Identify conclusion → Translate into logic → test for validity

Venn Diagram Conclusions: All A is B

If every region of A outside of B is shaded

Venn Diagram Conclusions: No A is B

If overlap A-B region is completely shaded

Venn Diagram Conclusions: Some A is B

If there is an X inside A-B

Venn Diagram Conclusions: Some A is not B

If there is an X inside A outside of B