semantics

There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

11/27/11 10Software

You now have to tools to appraise sentential arguments.

Let us run through how these might be used with two examples.

Example 1.

Consider the argument

If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.

First it should be symbolized

7/3/06

Some of these videos will use different logical symbols to the ones you are familiar with; for example, they use '∧' for 'and' (instead of either '&' or '.'). These minor display unfamilarities do not affect the principles and operations that are being explained.

11/26/11 10Software

Skills to be acquired in this tutorial:

To learn how compound sentences are true or false depending on the truth or falsity of their component sentences.

7/3/06

8/16/06 10Software

Skills to be acquired in this tutorial:

To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.

Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.