semantics

10/12/26

Reading

Hausman[2007] Logic and Philosophy Chapter 8

The Tutorial

A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.

There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.

There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,

Universe = {a,b,c}

10/12/26

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.

Tutorials 11 to 25: predicate logic, using the Hausman syntax.

Tutorials 1 to 10: sentential logic, using the Hausman syntax.

10/12/26 under construction

You now have to tools to appraise arguments to the level of detail offered by predicate logic.

Let us run through how these might be used with a long and difficult example.

Consider the argument

The Tutorial

The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}

The Tutorial

We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}

The Tutorial

A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.

There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.

There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,

Universe = {a,b,c}

10/12/26

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.

The Tutorial:

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

Truth can be discussed in more detail in predicate logic.

Tutorials 11 to 25: predicate logic, using the Copi syntax.