symbolization

2/5/08

Reading

Hausman[2007] Logic and Philosophy Chapter 10

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

Symbolization using the Universal Quantifier (of non relational English)

10 Software

Reading

Hausman[2007] Logic and Philosophy Chapter 10

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

Hausman[2007] Logic and Philosophy Chapter 7

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

Reading

Hausman[2007] Logic and Philosophy 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,

6/14/07 10 Software

Skills to be acquired in this tutorial:

To start learning how to symbolize sentences using predicate logic.

Reading

Hausman[2007] Logic and Philosophy 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.

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

1/24/06

eg Lander or Suber

The problem or issue here lies with the truth table for the conditional (or material implication) ³

There is the idea of setting up a code or convention or dictionary between atomic sentences and capital letters.

There are compound sentences, each of which has a main connective which connects its components.

There are five sentential logical connectives:

'∼' which translates back to 'it is not the case that...'

'.' which translates back to '... and ...'

'∨' which translates back to '... or ...'

'³' which translates back to 'if... then ...'

'≡' which translates back to '... if and only if ...'