symbolization

10/19/26

Tutorial 2 Example: How Experts Symbolize

Reading

Herrick[2000] The Many Worlds of Logic Chapter 17

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 sentence would be symbolized Tab.

10/13/26

Reading

Herrick[2000] The Many Worlds of Logic Chapter 16

Skill to be acquired in this tutorial:

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

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).

Reading

Herrick[2000] The Many Worlds of Logic Chapter 7

Tutorial

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

Beryl is wise. (ie adjective)

Beryl runs. (ie verb)

Beryl is a philosopher. (ie noun)

might be symbolized Wb, Rb, and Pb, respectively.

10/13/26

Skills to be acquired in this tutorial:

To start learning how to symbolize sentences using predicate logic.

Reading

Herrick[2000] The Many Worlds of Logic Chapter 7

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.

10/13/26

Skills to be acquired in this tutorial:

To learn how to symbolize arguments, and how to judge whether they might be invalid using truth-table methods.

Why this is useful:

We wish to appraise arguments, to do this we have to symbolize them first. Judging the invalidity of arguments by truth-table methods is not particularly important, but it does help to develop skills involving truth and lists of formulas.

Reading

Herrick[2000] The Many Worlds of Logic Chapter 5

10/13/26

Skills to be acquired in this tutorial:

Symbolizing compound sentences. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

Why this is useful:

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

10/13/26

Skills to be acquired in this tutorial:

To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic sentences.

Reading

Paul Herrick [2000] The Many Worlds of Logic ISBN: Chapter 1

Tutorial:

The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.

For example,

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

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