# symbolization

## Tutorial 11: Sketch of the second part of the course, and symbolizing propositions using predicate logic.

Topic
Logical System

2013

### Skills to be acquired in this tutorial:

To start learning how to symbolize propositions using predicate logic.

### The Tutorial:

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

## Predicate Logic: 15 Tutorials

Topic
Logical System

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

## Supplementary: The Paradoxes of Material Implication

Topic
Logical System

1/24/06

eg Lander or Suber

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

## Review

Topic
Logical System

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

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

There are five propositional logical connectives:

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

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

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

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

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

Topic
Logical System

## Tutorial 2: Symbolizing compound propositions

Topic
Logical System

9/1/12

### Skills to be acquired in this tutorial:

Symbolizing compound propositions. 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.

## Symbolizing Compound Propositions I

Topic
Logical System

8/25/12

Not all propositions are atomic propositions. Consider the proposition asserted by 'It is not the case that in 2011 the United States had a female President'. This is a true proposition, yet it is not an atomic one. It is made up of the atomic proposition 'in 2012 the United States had a female President' (which is false) and negation (expressed by 'It is not the case that...'), and the resulting compound proposition, which is the negation of a false proposition, is true.

There are several types of compound proposition.

## Symbolization Review

Topic
Logical System

8/26/12

[The core of this is from Hugues Leblanc and William A. Wisdom [1972] Deductive Logic p.111 and f.]

## Symbolize Relations

Topic
Logical System

8/26/2012

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.

## Symbolization Using the Quantifiers

Topic
Logical System

#### 8/26/2012

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).