Modus Ponens & more... Phil 101 Test #2
Conditional
"If, then" If antecedent, then consequent If P then Q ; P->Q Ex. If Paula helps him, then Quincy will pass H->P After the word "if" is where you start set up for ex.
Modus Ponens
"The mode of putting" ; put P, get Q Affirming the antecedent Ex 1. If P, then Q Ex 2. If S then O, S Therefore, O W -> B: If the weather is good, we can go to the beach. W: The weather is good. ---------- B: We can go to the beach.
Modus Tollens
"The mode of talking" Denying the consequent Take Q, take P Ex. If S then B Not B Therefore, not S S -> F: If there is smoke, there is a fire. ~F: There is no fire. ---------- ~S: There is no smoke.
A Claim:
(A)All S are P; All _____ are_____.
E Claim:
(E)No S are P; No____are_____.
I Claim:
(I)Some S are P ; Some___ are_____.
Affirming the Consequent
(Invalid) If P then Q. Q. Therefore, P. Ex. If taxes are lowered, I will have more money to spend. I have more money to spend. Therefore, taxes must have been lowered. FALSE
Denying the Antecedent
(Invalid) If P, then Q. Not P. Therefore, not Q. Ex. If it barks, it is a dog. It doesn't bark. Therefore, it's not a dog.
O Claim:
(O)Some S are not P ; Some____ are not____.
3 rules of a syllogism
1) Same number of (-)negative claims in premise as there are in the conclusion 2) Middle term MUST be distributed by 1 premise 3)Any term that is distributed in the conclusion of the syllogism must be distributed in its premises
Categorical Syllogism
3 terms in argument( Each term has to appear TWICE in argument) Ex. All Americans are consumers Some consumers are not democrats Therefor, some Americans are not consumers All A are C Some C are not D Therefor, some A are not C
How many forms do Categorical Statements come in?
4 standard forms; (A)All S are P (E)No S are P (I)Some S are P (O)Some S are not P
Antecedent
A thing or event that existed before or logically precedes another
Harder Test of Validity
A: All (S) are P E: No (S) are (P) I: Some S are P O: Some S are not (P) CIRCLED letters are DISTRIBUTED
Obverse of a Claim
Changing of a claim from affirmative to negative, or vice versa Ex. A: All Presbyterians are Christians No Presbyterians are not Christians E: No fish are mammals All fish are non-mammals I: Some citizens are voters Some citizens are non-voters O: Some contestants are not winners Some contestants are not winners
Two types of Arguments
Deductive & Inductive
Subjective Term In Categorical Statements
Goes into the first blank when writing statement or identifying it
Predicate Term In Categorical Statements
Goes into the second blank when writing statement or identifying it
Contradictory Claims
Referring to when A, E, I, and O Claims are at opposite diagonal corners
Contrary Claims in square of opposition
The A and E Claims; (Not both True) ; top of square
Subcontrary Claims
The I and O Claims ; (Not both False) ; bottom of square
Chain Argument
The conclusion links cause and an effect, while premise explains in between Ex. W -> M: "If you have a job, you will get money." M -> F: "If you have money, you can buy food." ---------- W -> F: "If you have a job, you can buy food." *** The consequent of 1 premise is the same as antecedent of the other
Weaker Argument
The less support the premise of an inductive argument provides for the conclusion; ONLY within a inductive argument
Undistributed Middle
The middle term, or the term that does not appear in the conclusion, is not distributed to the other two terms. All A's are C's. All B's are C's. Therefore, all A's are B's. Ex. All lions are animals. All cats are animals. Therefore, all lions are cats.
Stronger Argument
The more support the premise of an inductive argument provides for the conclusion; ONLY within a inductive argument
Deductive Arguments
The premises are intended to prove or demonstrate the conclusion
Inductive Arguments
The premises are intended to support the conclusion; In a good inductive argument, the premise makes the conclusion more likely to be true
Square of Opposition
Two categorical claims correspond to each other if they have the same predicate term (ONLY WORKS FOR CORRESPONDING CLAIMS)
Conversion
Used in E and I claims; When you find the converse of a standard form claim by switching the positions of the subject and predicate terms Ex. E: No Norwegians are Slavs No Slavs are Norwegians I: Some state capitals are large cities Some large cities are state capitals
Equivocation
Using an ambiguous term in more than one sense, thus making an argument misleading. Ex. I want to have myself a merry little Christmas, but I refuse to do as the song suggests and make the yuletide gay. I don't think sexual preference should have anything to do with enjoying the holiday.
Why do we put "Valid" in quotations when talking about arguments?
Valid is in "Quotations" because the argument can be wrong is the sense of factual evidence, but since the definition of validity says it isn't possible for for the premise to be true and the conclusion false.
Venn Diagram test of Validity
Venn diagram test with 3 circles -Two circles on top -One circle on bottom Subjective of conclusion on left Predicate of conclusion on right Middle term( not in conclusion but in both premise) on bottom ** Shaded area of diagram means nothing is in there
What is the best way to test validity within a categorical syllogism?
Venn diagram test with 3 circles -Two circles on top -One circle on bottom Subjective of conclusion on left Predicate of conclusion on right Middle term( not in conclusion but in both premise) on bottom ** Shaded area of diagram means nothing is in there
Sound Argument
When a deductive argument is valid and the premises are true; ONLY within a deductive argument
Unsound Argument
When a deductive argument is valid, but 1 or more premise is actually false; ONLY within a deductive argument
"Valid"
When it isn't possible for the premise to be true and the conclusion false.
Categorical Statement
relates two classes or categories, denoted by the subject term (S ) and the predicate term (P). ; Useful in clarifying and analyzing deductive arguments
