PHI 103 MWF 9:40
March 5, 2008
Set B: Paper Topic 3
In this paper, I will be discussing the validity and soundness of the following
argument:
An argument has a true conclusion or it does not. An argument has a true
conclusion only if it has a tautology as a conclusion. If it has a tautology as a conclusion,
then it is both valid and sound. An argument is invalid, if it has a false conclusion. If an
argument is invalid, then it has consistent premises. If the premises are consistent and the
conclusion is a contradiction, then the argument is invalid. If an argument has a
contradiction as a conclusion, then it is invalid. If an argument has a contradiction as a
conclusion, then it is unsound. Thus, if an argument is valid, then it is sound.
I will begin by putting the argument in standard logical form. To do this, I will
provide a symbolization and a dictionary:
A= an argument has a true conclusion
T= an argument has a tautology as a conclusion
V= an argument is valid
S= an argument is sound
P= an argument has consistent premises
C= an argument has a contradiction as a conclusion
Using this dictionary, the translation of the argument is as follows:
Av~A
A
T
T
(V&S)
~A
~V
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
~V
P
(P&C)
~V
C
~V
C
~S
______________
V
S
To prove that this argument is valid, I will use reverse truth tables. To do this, I
must start with the conclusion. To prove the argument invalid, the conclusion would have
to be false. V
S is false only when V=t (true) and S=f (false). So far, the argument is as
follows:
Av~A
A
T
T
(t&f)
~A
~t
~t
P
(P&C)
~t
C
~t
C
~f
______________
t
f
(F)
Next, we want the premises to be true, as an invalid argument must have true
premises and a false conclusion. There are three ways for the first premise to be true, so I
will skip over that one until we have better knowledge. I will skip to the fourth premise,
because we know that V=t, so ~A
~t. “~t” symbolizes “not true.” The only way for this
premise to be true with a false descendent is if the antecedent is false as well. Thus “A”
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 BOLTON
 Logic, Conclusion

Click to edit the document details