symbolization

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.

6/22/07

Reading

Bergmann[2004] The Logic Book Sections 7.7-7.8

[The core of this is from Leblanc and Wisdom [1972] p.117 and f.]

Symbolization using the Universal Quantifier (of non relational English)

10 Software

The Tutorial

Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.

6/18/07 10 Software

Skill to be acquired in this tutorial:

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

Reading

Bergmann[2008] The Logic Book Sections 7.4

The Tutorial

In Predicate Logic there are two new logical connectives, the Universal Quantifier (∀x) and the Existential Quantifier (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).

10 Software

In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,

6/14/07 10 Software

Skills to be acquired in this tutorial:

To start learning how to symbolize sentences using predicate logic.

Reading

Bergmann[2008] The Logic Book Sections 7.1-7.3

The Tutorial:

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.

Example only

Tutorial 16 Symbolization using the quantifiers.

1/27/09 10 Software

Skill to be acquired in this tutorial:

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

12/26/13

Skills to be acquired in this tutorial:

To start to learn about identities, the semantics of identities, and typical expressions in English that might use identities.

Why this is useful:

Reasoning with identity is vital for mathematics, philosophy, and many other areas.

12/19/20

Welcome!

The tutorials presented here look at some topics in logic to the level of intermediate to advanced Predicate Calculus. They build on the Tutorials of Easy Deriver which provided the introductory material to Propositional and Predicate Calculus.

The program, widgets, or Notes, should be accompanied by a suitable textbook, such as: