Julissa Massa
The purpose of this paper is to analyze the validity and soundness of the following argument:
If an argument is valid and has a true conclusion, then it is sound. If an argument is
sound, then it has a true conclusion. An argument is valid i
Julissa Massa
A valid argument is one where the truth of its premises guarantees the truth of its conclusion.
This does not imply that all valid arguments must be true and all invalid arguments must be false. This
simply means that the form of an argument
Truth Tables Statements
Example 1
Suppose we have the following compound statement: A(~A~B). We can determine the truth
value for this statement by setting up a truth table
Step 1
In this step, we are going to set up the initial setup and we are going to
Contradictions, Tautologies, and Validity
In order for an argument to be invalid, there must be an interpretation where
1.
2.
the premises are all true; and
the conclusion is false.
These two conditions lead to the paradoxes of validity. If an argument ha
Tautologies, Contradictions, and Categorical Syllogisms.
Remember our definition of a categorical syllogism. A categorical syllogism is an
argument with two premises and one conclusion. It includes three terms, a subject, predicate,
and middle term. These
Truth Tables Initial Setup
Suppose we have one simple statement, P. Since P is a declarative sentence, we know P is either
true or false. We can represent these two possibilities in the following manner:
P
T
F
Suppose we have two simple statements, P and
Mood and Figure
Each categorical syllogism can be identified by means of mood and figure.
The mood of a categorical syllogism is determined by the categorical statements used in that
syllogism. Each categorical statement has a letter identified with it:
C
Validity, Soundness, and Truth
In this course, we are very interested in the notion of deductive validity (or validity, for short).
Validity concerns the form of an argument.
Definition
An argument form is deductively valid if and only if:
1. When its pre
Invalidity
Just as validity does not guarantee truth, invalidity cannot guarantee falsity. Here is an example
of an invalid argument form:
Some M are P
Some M are S
Some S are P
Invalid argument forms can also have instances with true premises and a true
Truth Tables for Connectives
We have five connectives. These are the truth tables for our five connectives.
(1) negation
P
T
F
~P
F
T
A statement and its negation take opposite truth values.
(2) conjunction
P
T
T
F
F
Q
T
F
T
F
P&Q
T
F
F
F
A conjunction is
Categorical Syllogisms Terms
So far, we have been dealing with a particular type of argument. The type of argument that we
have been discussing is a categorical syllogism.
Definition
A categorical syllogism is an argument that consists of two premises and