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The normal contrast to deduction is [[induction]], whereby the two are posed as  distinct opposites. However, they are not so distinct as to be alien to each other. Rather, induction and deduction have a single common root from which they necessarily are operationally distinguished: the mind. So, in regard to formal logic in this root sense, a merely mechanical or electronic simulator of genuine mental operations does not possess either any actual deductive or actual inductive logic.

The normal contrast to deduction is [[induction]], whereby the two are posed as  distinct opposites. However, they are not so distinct as to be alien to each other. Rather, induction and deduction have a single common root from which they necessarily are operationally distinguished: the mind. So, in regard to formal logic in this root sense, a merely mechanical or electronic simulator of genuine mental operations does not possess either any actual deductive or actual inductive logic.

The most famous formal deductive rule goes as follows:

The most famous formal deductive rule goes as follows:

#Therefore, Q is not true.

#Therefore, Q is not true.

 

{{Cquote|A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said also to be sound. All arguments are either valid or invalid, and either sound or unsound; there is no middle ground, such as being somewhat valid.

A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said also to be sound. All arguments are either valid or invalid, and either sound or unsound; there is no middle ground, such as being somewhat valid.

Here is a valid deductive argument:

Here is a valid deductive argument:

The conclusion follows the word "So". The two premises of this argument would, if true, guarantee the truth of the conclusion. However, we have been given no information that would enable us to decide whether the two premises are both true, so we cannot assess whether the argument is deductively sound. It is one or the other, but we do not know which. If it turns out that the argument has a false premise and so is unsound, this won't change the fact that it is valid.

The conclusion follows the word "So". The two premises of this argument would, if true, guarantee the truth of the conclusion. However, we have been given no information that would enable us to decide whether the two premises are both true, so we cannot assess whether the argument is deductively sound. It is one or the other, but we do not know which. If it turns out that the argument has a false premise and so is unsound, this won't change the fact that it is valid.

== Truth Values in Sentential Logic ==

== Truth Values in Sentential Logic ==