semantics

6/6/09 10Software

Skill to be acquired:

To learn how to interpret simple predicate logic formulas as being true or false.

Why this is useful:

This helps in proving invalidity by the technique of displaying a counter-example.

Reading

Hausman[2007] Logic and Philosophy Chapter 8

The Tutorial:

In sentential logic, we just took it that each of the atomic sentences either is true or is false-- we did not look into the structure of the sentences.

Truth can be discussed in more detail in predicate logic.

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.