Week 6: Logic Flashcards
What is logic in the techincal sense, provide a new example.
Logic follows a sequential chain; drawing true conclusion from an initial true statement (deductive logic).
E.g., If humans breathe, then Bob breathes
The three reasons why people don’t apply logic
- Difficult, & rules are not used appropriately (leading towards formal fallacies)
- People refuse to follow rules (informal fallacies)
- Applicability; logic suitable for certain goals with certain kinds of knowledge, but unhekful with other instances
How is logic formal?
Logic deals with forms, and not content - it is general purpose, no matter content. **
Explain the function of material conditional.
Material conditional is a counteractance against the contradition brought about by the rule IF P THEN Q. If P is false, Q is true, but simply because P was never proven to be true, creating statements such as “if pigs had wings, then 2+2 = 5.” Thus, material conditioning is true within the truth table, however conditionally, Q cannot be true unless P is proven.
Explain the distinction between conditional and material conditonal
Material conditional is the strictest interpretation of the truth table, i.e., if P is false, then Q is true, since P never existed to prove if Q was false.
Whereby everyday conditional instances, if P is false, Q is reluctantly true because Q was never testified to prove if this was the case. i.e., If you drink turnip juice, you will never fall asleep
How does everyday language differ from mnemonic symbols used as connector in formal logic
Since words don’t have just one meaning and that situations can make words more ambiguous, understanding of formal language is affected.
E.g.,
Sat down and told me his life story, but logically it can be other way around
Soup or salad, but technically entitled to both
What are tautologies
Statements inherently true due to their logical structure, e.g., it is what it is - restating the same idea. They provide no new information
If John goes to Church, then it is Sunday, explain this through material conditional and also everyday conditional.
We can deduce that if John is at church, then we know its Sunday. However, if P is false, we simply deduce Q to be true because P never occurred. Technically this is true (material conditional), however, everyday conditional suggests that we must witness whether Q does occur or not.
Explain how P and Q is false or true through the propositional calculus
P and Q is true if both P and Q statements are true.
P and Q is false if both or any of P and Q is false
CONJUNCTIVE
Explain how P OR Q is false or true through the propositional calculus
P or Q is true if one or the other or both is true
P or Q is false if both are false.
DISJUNCTIVE
Explain how in the instance of if P is true, then Q is true, how this statement can be false
In this instance of a propositional calculus, it is dependent on whether Q does occur corresponsively.
E.g., if you asked me on a date, I would say no. This statement was false as she said yes (Q)
