Validity and Soundness

An argument is a series of statements meant to establish a claim.

A statement is any explicit declarative statement about a fact. It says that something is (or isn’t) the case. A premise is a statement used in an argument to establish a claim. An argument is valid if its premises necessarily lead to its conclusion.

An argument is sound if it is valid and that its premises are actually true. The two arguments by Socrates in The Apology being evaluated are as follows.Argument 1 Premise 1 – If Socrates corrupts the young, they or their relatives will accuse him. Premise 2 – His young followers do not accuse him and neither do their relatives. Conclusion – Therefore, Socrates has not corrupted the young.

Argument 2 Premise 1 – Either death is dreamless sleep or death is migration of the soul to some other place. Premise 2 – If the former, then there is no reason to fear death. Premise 3 – If the latter, then there is no reason to fear death. Conclusion – Therefore, there is no reason to fear death. Symbolic notation and truth tables are great tools to identify validity. In argument 1, the statement that Socrates has corrupted the youth can be abbreviated as ‘Y’.

The statement that either his young followers will accuse him or their relatives will accuse him can be translated as – either ‘F’ or ‘R’.In the second argument, the statement that death is dreamless sleep can be abbreviated as ‘D’. The statement death is a migration of the soul to some other place can be abbreviated as ‘M’ and the statement that there is reason to fear death can be abbreviated as ‘F’. When one translates statements into symbolic notation, one must be concerned not to associate with the expressions of the English language; the letters or symbols should be in the purest form of its definition. Symbolic notation is a great time-saver in argumentation. It prevents logical confusion especially when dealing with complex arguments.

A logical operator is a symbol used to connect two or more statements in way, such that the compound statement produced has a truth value dependent on the respective truth values of the original statements. In order to know the truth value of the proposition which results from applying a logical operator, all that needs to be known is the definition of the operator and the truth value of the proposition. There are five major logical operator; ~ symbolizes negation, & symbolizes conjunction, v symbolizes disjunction, ? symbolizes conditional, and ? indicates bi-conditional. Considering these logical operators and the truth values of the statements in argument 1 and 2, we derive the following.For any logical statement, there can only be two values; either “True (T)” or “False (F)”. Any logical statement which contains a finite number of logical variables can be evaluated using a truth table which lists all possible values of the variables.

It is important to understand that the premises of an argument do not actually have to be true in order for the argument to be valid. When one constructs an argument, he/she must aim to construct one that is not only valid, but also sound.A sound argument is on that is not only valid, but each of its premises are actually true. Argument 1 and 2 are valid arguments, however they are not sound ones. In argument 1, if Socrates has corrupted the young, it need not be the case that his young followers or their relatives will always accuse him.

Socrates also does not have any power to make anyone to follow him, and the fact that he has young followers show that his young followers believe in him and do not feel corrupted because of him.In argument 2, Socrates claims that death is either dreamless sleep or migration of the soul to another place. No person for certain knows what happens after death. To know whether death is dreamless sleep or migration of the soul to another place is impossible because no one can communicate with the dead. Death definitely cannot be considered a dreamless sleep because sleeping includes waking up at some point.

It would not make sense to say that a corpse is just sleeping at the moment. Therefore, arguments 1 and 2 are both unsound arguments.To assess any argument, one should do the following tests. Firstly, one must find out if the premises provide support for the conclusion by methods such as truth tables or by just examining the form of the argument.

If the premises do, the argument is valid. Then he/she must ask whether the premises are true in reality. Only if the argument passes both these test is it sound. If an argument does not pass these tests, the conclusion may still be true, despite the no support for its truth is given by the argument.