symbolization

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 ...'

8/29/06

Tutorial 2 Example: How Experts Symbolize

[This is a film-- press the 'play' symbol.]

11/26/11 10 Software

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.

8/2/08

Tutorial 1 Exercise 2

[What is shown below is a Quicktime Movie, with sound. Your computer should be able to run this. If you are having trouble, check with Quicktime or Quicktime download and equip your machine for viewing Quicktime. If you have external speakers, or similar, you may need to turn them on and turn the volume up.]

11/26/11 10 Software

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

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapters 1, 2.1

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,