Today’s Topics

1 / 16

# Today’s Topics - PowerPoint PPT Presentation

Today’s Topics. Symbolizing conditionals and bi-conditionals Other complex symbolizations. Unless. Conditional. A conditional is composed of two elements, the antecedent (the ‘if’ part of an if, then, statement) and the consequent (the ‘then’ part)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Today’s Topics

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Today’s Topics
• Symbolizing conditionals and bi-conditionals
• Other complex symbolizations.
• Unless
Conditional
• A conditional is composed of two elements, the antecedent (the ‘if’ part of an if, then, statement) and the consequent (the ‘then’ part)
• A conditional is true if either the antecedent is false or the consequent true
If

Given that

Insofar as

Provided that

So long as

In case

Follows from

Is implied by

Whenever

Is a necessary condition for

Terms that Precede the Antecedent
Then

Only if

It follows that

Implies

Means that

Is a sufficient condition for

Terms that Precede the Consequent
The language of necessary and sufficient conditions is the language of conditionals.
• Sufficient conditions are antecedents of conditionals. Necessary conditions are consequents of conditionals.
• P is a sufficient condition for Q
• P  Q
• P is a necessary condition for Q
• Q  P
Biconditional
• A biconditional is composed of two elements
• A biconditional is true when the elements agree in truth value (both true or both false)
Biconditionals are introduced with the words “if and only if” or “is necessary and sufficient for”

P is both necessary and sufficient for Q

(P is necessary for Q) AND (P is sufficient for Q)

(Q  P) & (P  Q)

(P if Q) and (P only if Q)

P Q (P if and only if Q)

Try some symbolizations
• Download the Handout labeled Conditional Study Guide and attempt the exercises
• Post some of your answers to the bulletin boards and discuss them
Symbolizing “Neither Nor” and “Not Both”
• We have two different ways to symbolize both ‘neither nor’ and ‘not both’.
DeMorgan’s Law (1st Version)
• The negation of a disjunction is equivalent to a conjunction of the negations of the disjuncts.
DeMorgan’s Law (2nd Version)
• The negation of a conjunction is equivalent to a disjunction of the negations of the conjuncts
UNLESS (the word of the Lorax!)
• For a logician, unless means ‘or.’ And ‘or’ is inclusive unless otherwise specified.
• Yes, this use of ‘unless’ violates our common use, but logic is a normative discipline and often the logician wishes to reform ordinary use.
• When you see ‘unless’ in a sentence, replace it with a wedge! You can’t go wrong doing that.
• Download the Handout on Unless and see what havoc this word can wreak!
Key Ideas
• Symbolizing conditionals
• Other complex symbolizations
• Unless