Karteikarten
PHL 134
Karten in diesem Stapel (28)
- 1RAAReductio Ad Absurdum
Reduction to absurdity
Assume the opposite of what you're trying to get and derive a contradiction.
My assumption was incorrect.
You end up with the negation of your assumption. - 2How to work out how many rows are needed on a truth tableNumber of sentence letters (P, Q, R) (n)
2 to the power of n
(P, Q, R) =3
2x2=4x2=8
8 Rows - 3What does IPLI mean?Invalidating Propositional Logic Interpretation
- 4TautologyAn argument is true no matter what (according to the truth table)
- 5ContingencyTrue in some cases but not in others (according to the truth table)
- 6SoundnessAnything that is syntactically valid is semantically valid.
The rules of inference only prove the things they should be able to prove.
If you can prove it with a Proof then you can prove it with a Truth Table.
The rules we have are correct. - 7MetatheoreticalThings that are proved about the theory
- 8CompletenessThe idea that PL is complete with the rules we have.
We can prove everything we should be able to prove!
Anything that is semantically valid is also syntactically valid.
The rules we have are sufficient - 9Sound ArgumentA valid argument that has factually true premises
- 10Truth table rules for && is only true when both conjuncts are true
- 11Truth table rules for -->--> is only false when the antecedent is true and the consequent is false
- 12Truth table rules for <-->True when both sides have the same truth value (both true or both false)
- 13BivalenceA semantic principle in language.
Each and every sentence has exactly one of two truth values. Either true or false (but not both and not neither). - 14Deductive argumentsArguments that aim for validity
- 15Binary connective~
Negation - 16Question TextAnswer Text
- 17Disjunctionv
or - 18Conditional-->
If...then... - 19Biconditional<-->
... If and only if ... - 20How to prove a conditionalAlways assume the antecedent and try to derive the consequent
- 21ContradictionConjunction of any formula with its negation
- 22Golden Rule1. Try simple rules
2. Do you need to get a conditional? If so use CP (assume antecedent, derive consequent)
3. Do you already have a disjunction? If so use vE (assume each disjunct and derive the conclusion from each)
3. Are you trying to get a negation or something else you can't get by other means? Use RAA. (Assume the opposite and derive a contradiction) - 23MonotonicityIf a given formula follows from a particular set of formulas then the same formula follows from any augmentation of that set of formulas.
(Hypotheses of any derived fact may be freely extended with additional assumptions) - 24Law of excluded middlefor any proposition either that proposition is true its negation is true.
- 25Truth table rules for vDisjunction is only false if both disjuncts are false
- 26Valid argumentThe structure of an argument is what makes it valid.
- 27Rules for the Short-cut MethodMake the main connective of the premises true and the main connective of the conclusion false.
Then try to prove it.
(This will be proving that the argument is invalid if it's able to be completed) - 28How do you know what the IPLI is?IPLI shows how the argument is invalid.
If there is a case where both premises are true and the conclusion is false it means that the argument is invalid
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- Karteikarten am PHL 134, erstellt von Aimee Downing am 02/09/2016.
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