Lps 29/philosophy 29

Front 1

logic

Back 1

analysis and appraisal of arguments.

Front 2

argument

Back 2

a set or collection of statements expressed be a declarative sentence, one of which is distinguished as the conclusion, the rest, if any, are called premises. valid/invalid

Front 3

premises

Back 3

intended to provide support or evidence for the conclusion.

Front 4

deductive argument

Back 4

argument in which the premises are intended to establish the absolute truth of the conclusion.

Front 5

inductive argument

Back 5

argument in which the premises are intended to establish a probable truth of the conclusion.

Front 6

Valid

Back 6

if it is impossible (contradictory) to have true premises but a false conclusion. an argument isn't valid because it's true, it's valid because the premises and conclusion are logical.

Front 7

philosophy

Back 7

reasoning about the ultimate questions in life.

Front 8

sound

Back 8

valid and every premise is true.

Front 9

statements

Back 9

true/false

Front 10

syllogistic logic

Back 10

studies arguments whose validity depends on "all", "no", "some" and similar notions. involves propositions (called categorical propositions) that express certain relations of inclusion or exclusion between subjects and predicates.

i.e. All dogs go to heaven. = All D are H.

Front 11

wffs

Back 11

well-formed formulas. capital letters.

Front 12

4 forms of wffs

Back 12

aka categorical propositions

All A are B.
No A are B
Some A are B.
Some A are not B.

Front 13

alternative definitions of validity

Back 13

-argument is valid if it has a valid form.
-an argument form is valid if there are no instances of it with true premises and a false conclusion.

Front 14

syllogism

Back 14

an argument consisting of categorical compositions. generally has two premises.

Front 15

syllogistic language

Back 15

all, some, not, no.
A, B, C, D.....,
same letter represents same idea.

Front 16

Venn Diagrams

Back 16

diagrams only with traditional syllogisms. syllogism is valid iff drawing the premises automatically draws the conclusion. shade ares known to be empty. put an x where one entity is known to exist. if x can go in two different places, argument is invalid, place it where it will bring an invalid conclusion.

Front 17

words hinting at premises

Back 17

because, for, since, after all, I assume that, as we know, for these reasons.

(what is argued from)

Front 18

words hinting at conclusions

Back 18

hence, thus, so, therefore, it must be, it can't be, this proves (or shows) that...

(what is argued to)

Front 19

principle of clarity

Back 19

interpret unclear reasoning in the way that gives the best argument.

(if some letters are only stated one, add implicit arguments.)

Front 20

propositional logic

Back 20

studies arguments whose validity depends on "if-then", "and", "both", "either...or", "not", "iff" and similar notions.

i.e. All dogs go to Heaven. = D

Front 21

forming wffs

Back 21

1. Any capital letter is a wff
2. prefixing any wff w/~ is a wff.
3. joining any two wffs by . (dot), v, horseshoe, or _= and enclosed in parenthesis is a wff.

Front 22

truth table

Back 22

logical diagram for a wff. lists all possible truth-value combos for letters and says whether the wff is true or false in each case.

Front 23

truth table for add (•)

Back 23

PQ (P•Q)
00 0
01 0
10 0
11 1

(P•Q) is a conjunction
P & Q are its conjuncts

Front 24

truth table for v

Back 24

PQ (P v Q)
00 0
01 1
10 1
11 1

(P v Q) is a disjunction
P & Q are it's disjuncts

Front 25

~

Back 25

not. ~P = Not P

Front 26

•

Back 26

both... and. (P•Q) = Both P and Q

Front 27

v

Back 27

either... or. (P v Q) = Either P or Q.

inclusive "or": A or B or both (A v B).
exclusive "or": A or B but not both ((A v B) • ~ (A • B))

Front 28

horseshoe

Back 28

If... then. (P horseshoe Q) = If P then Q.

Front 29

_=

Back 29

iff. (P_= Q) = P iff Q.

Front 30

truth table for horseshoe

Back 30

PQ (P horseshoe Q)
00 1
01 1
10 0
11 1

(P horseshoe Q) is conditional.
P is antecedent
Q is consequent

Front 31

why is (1 horseshoe 0) false (=0)?

Back 31

falsity implies anything:
(0 horseshoe )= 1

anything implies truth
( horseshoe 1) = 1

truth doesn't imply falsity
(1 horseshoe 0) = 0

Front 32

truth table for iff

Back 32

PQ (P _= Q)
00 1
01 0
10 0
11 1

P_= Q is biconditional. both have same truth value.

Front 33

truth table for ~

Back 33

P ~P
0 1
1 0

~P is negation

Front 34

connectives

Back 34

grammatical devices for building new sentences from old ones.
_____ and______ >truth-functional

a connective is truth-functional iff the truth value of an expression "A and B" is determined (is a function of) the truth values of A and B).

Front 35

Different ways to say All A is B

Back 35

-Every (each any) A is B
-Whoever is A is B
-A's are B's
-Those who are A are B
-If a person is A, then he is B
-If you're A, then you're B
-No one/Nothing is A unless B
-A thing isn't A unless it's B
-It's false that some A is not B

Front 36

Different ways to say All A is B (switching A and B)

Back 36

-Only B's are A's
-None but B's are A's

Front 37

Different ways to say No A is B

Back 37

-A's aren't B's
-Every (each, any) A is non-B
-Whoever is A isn't B
-If a person is A, then isn't B
-If you're A, you're not B
-It's false that some A is B
-No one that's A is B
-There isn't a single A that's B
-Not any A is B
-It's false that there's an A that's a B

Front 38

Different ways to say Some A is B

Back 38

-A's are sometimes B's
-There are A's that are B's
-One or more A's are B's
-It's false that no A is B
-Some A is not B
-One or more A's aren't B's
-There are A's that aren't B's
-Not all A's are B's
-It's false that all A is B

Front 39

truth table validity

Back 39

truth table test is valid if no line is 110 (in 2-premise) or 1110 (in 3-premise) etc.

Front 40

main connective

Back 40

the main connective of a compound wff is the last connective applied in the construction of the wff.

Front 41

contingent statement

Back 41

one that logically could've been true or false. A wff whose truth table has some cases true and some cases false.

Front 42

law of excluded middle

Back 42

every statement is true or false, excludes the gray areas.

Front 43

tautology

Back 43

truth table true in all cases. or iff the line in truth table directly under main connective consists of all 1's.

Front 44

self-contradiction

Back 44

false in all cases. if column under main connective consists of all 0's.

Front 45

S-Rules

Back 45

used to simplify statements.

Front 46

(P•Q)

Back 46

P, Q

Front 47

(~P•~Q)

Back 47

~P, ~Q

Front 48

~(P v Q)

Back 48

~P, ~Q

Front 49

~(~P v ~Q)

Back 49

P, Q

Front 50

~(P > Q)

Back 50

P, ~Q

Front 51

I-rules

Back 51

used to infer a conclusion from two premises

Front 52

~(P•Q)
P

Back 52

~Q

Front 53

~(P•Q)
Q

Back 53

~P

Front 54

~(P•Q)
~P

Back 54

no conclusion

Front 55

(P v Q)
~P

Back 55

Q

Front 56

(P v Q)
~Q

Back 56

P

Front 57

(P v R)
L

Back 57

no conclusion

Front 58

(P > Q)
P

Back 58

Q. modus ponens - affirming mode.

Front 59

(P > Q)
~Q

Back 59

~P. modus tollens. denying mode.

Front 60

(D > A)
~D

Back 60

no conclusion

Front 61

(D > A)
A

Back 61

no conclusion

Front 62

(P = Q)

Back 62

(P > Q) (Q > P)

Front 63

~(P = Q)

Back 63

(P v Q) ~(P•Q)

Front 64

RAA

Back 64

reducto ad absurdum (reduction to absurdity) which says that an assumption that leads to a contradiction must be false.

Front 65

refuatation

Back 65

a set of truth conditions making the premises all true and conclusion false.

Front 66

quantificational logic

Back 66

studies arguments whose validity depends on "all" "no" "some" and similar notions.

Front 67

general terms

Back 67

use capital letters for describing categories. i.e. charming, Italian.

Front 68

singular terms

Back 68

use small letters, terms that pick out a specific. i.e. this child, the richest Italian.

Front 69

capital letter alone. i.e. S

Back 69

not followed by small letters. represents a statement

Front 70

a general term

Back 70

capital letter followed by small letter

Front 71

a relation

Back 71

capital letter followed by two or more small letters.

Front 72

constant

Back 72

small letters from a to w.

Front 73

variable

Back 73

a small letter from x to z. unspecified member of a class of things.

Front 74

quantifier

Back 74

a sequences of the form (x) or (Ex) where any variable may replace x.

Front 75

universal quantifier

Back 75

(x) is a universal quantifier. it claims that the formula that follows is true for all values of x.
(x)Ix = for all x, x is Italian
= all are Italian.

Front 76

existential quantifier

Back 76

(Ex). it claims that the formula that follows is true for at least one value of x.
(Ex)Ix = For some x, x is Italian
= some are Italian.

Front 77

(x)

Back 77

statements that begin with all (every)

Front 78

~(x)

Back 78

statements that begin with not all (not every)

Front 79

(Ex)

Back 79

statements that begin with some

Front 80

~(Ex)

Back 80

statements that begin with no

Front 81

All are rich or Italian

Back 81

(x)(Rx v Ix)

Front 82

Not everyone is non-Italian

Back 82

~(x)~Ix

Front 83

Some aren't rich.

Back 83

(Ex)~Rx

Front 84

No one is rich and non-Italian

Back 84

~(Ex)(Rx•~Ix)

Front 85

with "all" and "is" in QL

Back 85

> for middle connective. other cases use •

Front 86

universe of discourse

Back 86

the set of entities that words like "all" "some" and "no" range over in a given context.

Front 87

reverse squiggle

Back 87

~(x)Fx -> (Ex)~Fx

~(Ex)Fx -> (x) ~(Ex)

Front 88

drop existential

Back 88

(Ex)Fx -> Fa

Front 89

drop universal

Back 89

(x)Fx -> Fa