Validity And Soundness Essay

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Paper Topic 3

For this paper I will break down the following argument in terms of validity and soundness:

If an argument has a true conclusion, then it is both valid and sound. If an argument is sound, then it is valid. An argument will have a true conclusion if it is sound. An argument has a false conclusion only if it is valid. If an argument has a false conclusion, then it is invalid. An argument is both valid and invalid. Therefore, an argument is sound if and only if it is sound.

I have prepared a dictionary to more clearly distinguish the different premises. Here is my dictionary is standard logical form.

“C” represents a consistent premise
“S” represents a sound argument
“V” represents a valid argument

Here is the argument in standard logical form.

V→S
(V&C) →S
S→C
~C→(V&~S)
~S→~V
V&~V
C→C

The truth tables for the previous arguments can be located in the appendix. The truth table is used to examine the validity of the arguments. All of the arguments are valid because there are no occurrences in which the premises are true and the conclusion is false.

Using two examples from the truth table I can explain why they are valid.

V & ~V C → C
T F F T T T
T F F T T T
T F F F T F
T F F F T F
F F T T T T
F F T T T T
F F T F T F
F F T F T F …show more content…

There are two conditions a statement must meet to be valid. The first is that all premises must be true and secondly the statements conclusion must be false. A contradiction statement is false in every connotation making it logically false. Within the truth table there happens to be contradictions. For V&~V the conclusions are false in every statement. The opposite of a contradiction is a tautology. A tautology is when every interpretation is true. In the example of C→C the first condition is not met because there are four instances where both premises are false but the conclusion is

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