Like this presentation? Why not share!

# 6.4 Truth Tables For Arguments

## by Nicholas Lykins, Computer Science Research Assistant at Kentucky State University on Jun 05, 2009

• 3,203 views

Course lecture I developed over section 6.4 of Patrick Hurley\'s "A Concise Introduction to Logic".

Course lecture I developed over section 6.4 of Patrick Hurley\'s "A Concise Introduction to Logic".

### Views

Total Views
3,203
Views on SlideShare
3,202
Embed Views
1

Likes
0
0
0

### 1 Embed1

 http://www.slideshare.net 1

### Categories

Uploaded via SlideShare as Microsoft PowerPoint

## 6.4 Truth Tables For ArgumentsPresentation Transcript

• 6.4 Truth Tables for Arguments
• Process for constructing tables for arguments
• First, symbolize the arguments using symbols to represent the different propositions.
• Example:
• If I’m sick, then I’ll have a bad day. I’m sick. Therefore, I’ll have a bad day.
• P > Q
• P
• --------------
• Q
• Next, write out the argument, using a backslash to separate each premise and two backslashes between the last premise and the conclusion.
• Example:
• P v Q / P > Q // ~P · Q
• Use the rules for truth tables to draw a table for the entire statement, treating the whole thing like it’s one big logical equation.
• Process, continued
• Lastly, see if there’s at least one line where all of the premises are true and the conclusion is false. If there is, then the whole equation is invalid.
• If no line exists with true premises and a false conclusion, then the argument has to be valid.
• Process, continued
• Example:
• If murderers run free, then there will be deaths everywhere.
• Murderers run free.
• Therefore, there will be deaths everywhere.
• M > Q
• M
• -----------------
• Q
• M > Q / M // Q
F F F T F T F T T F F T F F T T T T T T Q // M / Q > M
• Miscellaneous points on validity
• An argument with inconsistent premises is always valid, regardless of the conclusion.
• Inconsistent = No line with all true premises.
• Invalid = True premises, false conclusion.
• So, No true premises = no invalidity.
• An argument with a tautologous conclusion is also always valid, regardless of its premises.
• Tautologous = Always true.
• Invalid = True premises, false conclusion.
• So, always true conclusion = no chance of invalidity.
• Inconsistent premises
• Example:
• The sky is blue.
• The sky is not blue.
• -------------------------
• Therefore, Paris is the capital of France.
• S
• ~S ---------------
• P
• S / ~S // P
• The premises in this argument are inconsistent so the whole argument is valid, regardless of its conclusion.
T F T F P // S ~ / S F F T F F T F T T T F T
• Tautologous conclusion
• Example:
• Bern is the capital of Switzerland.
• -------------------------
• Therefore, it is either raining or it is not raining.
• B
• ----------------
• R v ~R
• B // R v ~R
• The conclusion here is tautologous, so the whole argument is valid regardless of its premises.
F T T F F T F T T F F T T F T T F T T T R ~ v R // B