TEST #2 Flashcards
logical operators and argument forms (ill-formed argument, invalid argument, non-cogent, cogency, conjunction, contraposition, universal modus ponens, biconditional, hypothetical syllogism) ( + original arguments using them)
what are invalid forms of arguments
the truth of the premises don’t guarantee the truth of the conclusion
denying the antecedent
affirming the consequent
truth vs rational strenght of premises
- evaluating the truth- value of a premise and conclusion is different from evaluating the rational strength of arguments
- it’s one thing to ask whether statements are true or not, but its another to ask: if those statements were true, what would that mean for the conclusion?
standard form
STANDARD FORM: arguments written out as consecutively numbered premises and conclusions, with justifications for each line in the argument stated
- provides a clear reconstruction of the argument (interpreting and rewriting an argument), which is essential for evaluating the argument (deciding whether or not the argument is a good argument)
benefits of standard form:
1) helps exclude any extra non-argument material
2) helps include unstated/missing premises
3) helps encourage clearer and precise formulation of premises and conclusion
4) helps make discussion of argument more convenient since each element is numbered
components:
- individually numbered premises and conclusion
- only one premise or conclusion per line
- the word “therefore” or equivalent symbol before the conclusion
- horizontal line between premises and conclusion
- brackets of the conclusion to show which premise the conclusion is supported by
deductive argument
DEDUCTIVE ARGUMENT: aims to provide a logically conclusive support for the conclusion
- it is impossible for the premises to be true, and the conclusion false
- shows that if the premises are true, the conclusion has to be true
well-formed argument
WELL-FORMED ARGUMENT: an argument is well-formed if and only if the argument is valid or cogent
- arguments whose conclusion does logically follow from its premises
- valid and cogent arguments
validity / a valid argument
- validity is a feature an argument either has, or doesn’t have
- in logic, validity applies only to arguments and the logical relationship between the premises and conclusions, not the premises or conclusion individually or their truth value
- a valid argument can have false premises and a false conclusion
- a valid argument is considered to be truth-preserving ( if premises are true, conclusion is true)
VALIDITY: an argument is deductively valid if and only if it is impossible for all the premises to be true, and the conclusion false
- A1) IF the premises are true, then the conclusion must be true as well
- A2) the conclusion logically follows the premise
- A3) in a world where the premises are all true, the conclusion is GUARANTEED to be true as well
invalid argument
INVALID ARGUMENT: it is possible for the premises to be true, and the conclusion to be false
- the premises dont guarantee the truth if the conclusion
validity test
VALIDITY TEST: the way in which we test if an argument is valid or not
1) Assume that the premises are all true. Would the conclusion have to be true as well?
2) If the answer is “yes” then the argument is valid. If the answer is “no” then the answer is invalid
is validity related to truth-value?
- No. a valid argument can have false conclusion and false premises.
- No. We don’t even have to know the truth-value of the premises and conclusion. as long as we evaluate the logical relationship between the premises and conclusion
-the point of validity is not whether each premise/conclusion is true or false, but rather that if the premises were true, would thy guarantee the truth of the conclusion?
sentential connectives + 5 types (dont explain)
SENTENTIAL CONNECTIVES: logical system in which sentences are not broken down into smaller units
- the letters stand for whole sentences
- use of UPPERCASE LETTERS
- the whole conclusion is found inside the premise
COMPOUND STATEMENTS: combination of two or more simpler sentences (we abbreviate them by using A and B)
1) conjunction
2) disjunction
3) negation
4) conditional
5) biconditional
predicate logic
opposite of sentential connectives
PREDICATE LOGIC: logical system in which sentences are broken down in subunits such as subjects and predicates (descriptive phrases)
SMALL LOWERCASE LETTERS (x): particular person or thing
BIG UPPERCASE LETTERS (A, B, C): descriptive phrases/characteristics
conjunction (sentential connective)
1) CONJUNCTION
- P and/& Q
- they are compound statements composed of two parts call the conjuncts
- ex. Today is tuesday and I am in class.”
disjunction (sentential connective)
2) DISJUNCTION
- P or/v Q
- they are compound statements composed of two parts called the disjuncts
- ex. either the picnic was cancelled or it was sunny
negation (sentential connective)
3) NEGATION
- Not P / ~ P
- saying the statement P is false/not the case
- ex. it is not sunny
conditional (sentential connective)
4) CONDITIONAL
- If P, then Q / If P -> Q
- if P happens, Q is guaranteed to happen (Q depends on P) (P guarantees Q)
- conditionals do not assert that either the antecedent or the consequent is true. they merely state a logical relationship between P and Q
- they are compound statements composed of two parts:
- ANTECEDENT: what follows the “if”
- CONSEQUENT: what follows the “then”
- ex. if it rains, then the picnic will be cancelled
conditionals are not always expressed in their logical form
- ex. since your lease expired, the landlord is free to raise the rent
- ex. being a teenager means you have lots of problems
- ex. anyone who likes logical is a fool
- ex. the truth of evolution implies the falsity of the Bible
- ex. whenever i drink coffee, i get antsy
“IF” introduces the antecedent, no matter where it occurs in a statement
- ex. “I’ll find the material difficult IF i skip a class”
- “ONLY IF” introduces the consequent, no matter where it occurs in a statement
- ex. “I will buy the giant TV ONLY IF the price drops”
- this should be written as Q -> P
biconditional (sentential connective)
5) BICONDITIONAL
- P if and only if Q
- if P then Q, if Q then P
- ex. you can enter the club if and only if you have legitamate ID
11 valid argument patterns (just list)
VALID ARGUMENT PATTERNS: common patterns shared by many deductive arguments
- help determine if an argument is deductive
- help determine if an argument is valid or invalid
- this is a means to an end: evaluating an argument
1) argument by elimination
2) conjunction
3) simplification
4) affirming the antecedent (modus ponens)
5) denying the consequent (modus tollens)
6) hypothetical syllogism
7) contraposition
8) universal modus ponens
9) universal modus tollens
10) universal hypothetical syllogism
11) universal ruling out
1) argument by elimination
- P v Q
- ~ P
:. 3. Q
(from 1, 2) - P v Q
- ~ Q
:. 3. P (from 1, 2)
ex. 1. either it will rain today or it will snow today
2. it will not snow today
therefore,
.: 3. it will rain today
2) conjunction
- P
- Q
:. 3. P & Q
ex, 1. I have a dog
2. I have a cat
therefore,
:. 3. I have a dog and a cat