Elementary Logic Ch. 1-3

Front 1

Therefore

Back 1

Conclusion indicator

Front 2

Thus

Back 2

Conclusion indicator

Front 3

So

Back 3

Conclusion indicator

Front 4

Hence

Back 4

Conclusion indicator

Front 5

For this reason

Back 5

Conclusion indicator

Front 6

Accordingly

Back 6

Conclusin indicator

Front 7

Consiquntly

Back 7

Conclusion indicator

Front 8

This being so

Back 8

Conclusion indicator

Front 9

It follows that

Back 9

Conclusion indicator

Front 10

The moral is

Back 10

Conclusion indicator

Front 11

Which proves that

Back 11

Conclusion indicator

Front 12

Which means that

Back 12

Conclusion indicator

Front 13

From whichwe can infer that

Back 13

Conclusion indicator

Front 14

As a result

Back 14

Conclusion indicator

Front 15

In conclusion

Back 15

Conclusion indicator

Front 16

For

Back 16

Premise indicators

Front 17

Since

Back 17

Premise indicators

Front 18

Because

Back 18

Premise indicators

Front 19

Assuming that

Back 19

Premise indicators

Front 20

Seeing that

Back 20

Premise indicators

Front 21

Granted that

Back 21

Premise Indicators

Front 22

This is true because

Back 22

Premise indicators

Front 23

The reason is that

Back 23

Premise indicators

Front 24

For the reason that

Back 24

Premise indicators

Front 25

In view of the fact that

Back 25

Premise indicators

Front 26

It is a fact that

Back 26

Premise indicators

Front 27

As shown by the fact that

Back 27

Premise indicators

Front 28

Given that

Back 28

Premise indicators

Front 29

Inasmuch as

Back 29

Premise indicators

Front 30

One cannot doubt that

Back 30

Premise indicators

Front 31

Formation Rule 1

Back 31

Any sentence letter is a wff.

Front 32

Formation Rule 2

Back 32

If phi is a wff,

then

~ phi is also a wff.

Front 33

Formation Rule 3

Back 33

If phi and psi are wffs,

then so are

(phi & psi), (phi V psi), (phi -> psi), and (phi <-> psi).

Front 34

(~R)

Back 34

Not a wff. Brackets are introduced only with binary operations (rule 3).

Front 35

PQ

Back 35

Not a wff. Two or more sentence letter can produce a wff only in combination with a binary operator (rule 3).

Front 36

((P->(Q))

Back 36

Not a wff. No rule allows us to surround sentence letters with brackets.

Front 37

(P V Q V R)

Back 37

Not a wff. Rule 3 allows us to combine only two sentence letters at a time.

Front 38

If

Back 38

Consequent before the antecedent.

Sufficient condition.

Implies that there are other ways to satisfy the condition, this is just one.

Front 39

Only if

Back 39

antecedent before the consequent

Necessary condition.

The consequent will only be true under the condition that the antecedent is true. This implies that this is the ONLY way to satisfy the condition.

Front 40

If and only if

Back 40

antecedent/consequent order is irrelevant.

Sufficient and necessary condition.

Combines both conditions, 'if' and 'only if'.

Front 41

Argument

Back 41

is a sequence of declarative sentences including:

one conclusion

AND

one or more premises

that are supposed to provide evidence for the conclusion

Front 42

Deductively Valid

Back 42

an argument is DV if it is impossible for the premises to be true but the conclusion false.

Front 43

Inductively Probable

Back 43

an argument is IP if the conclusion is probably true if the premises are true; an argument is IP to varying degrees

Front 44

Connectives

Back 44

and (conjunction)

or (disjunction)

if (conditional)

if...then (conditional)

if and only if (bi-conditional)

not (negation)

Front 45

Conditional

Back 45

Statements formed by if..then.
The statement following 'if' is called the antecedent; the other statement is the consequent.

If (antecedent) then, (consequent)

Front 46

Bi-Conditional

Back 46

Statements formed by 'if and only if'.
A conjunction of two conditionals.

If and only if (consequent) then, (antecedent)

Front 47

Truth table for conjunction

Back 47

a conjunction is true if both of its conjuncts are true, and false otherwise

phi psi phi&psi
T T T
T F F
F T F
F F F

Front 48

Truth table for a disjunction

Back 48

a disjunction is true if at lease one of its disjuncts is true, and otherwise false.

phi psi phiVpsi
T T T
T F T
F T T
F F F

Front 49

Truth table for conjunctions

Back 49

A conjunction (&) is true if both of its conjuncts (psi, phi, P,Q...) are true, and otherwise false

Front 50

Truth table for disjunctions

Back 50

A disjunction (V) is true if at least one of tis disjuncts is true, and false otherwise

Front 51

P -> Q

Back 51

has the same meaning as ~(P&~Q)

Front 52

Truth table for material conditionals

Back 52

A material conditional (->) is false if its antecedent is true and its consequent false; otherwise it is true.

NB: as for the biconditional, the form P<->Q means the same thing as (P->Q) & (Q->P).

Front 53

Formula for truth tables

Back 53

2 to the n

Front 54

Truth table for bi-conditional

Back 54

if the two components have the same truth value then they are true; otherwise, false

Front 55

counterexample

Back 55

a possible situation in which the conclusion of an argument or argument form is false while the assumptions are true. a counterexample showe the argument or argument form to be invalid.

Front 56

tautology

Back 56

a wff of propositional logic whose truth table contains only T's under its main operator. derivatively, any statement whose formalization is such a wff.

Front 57

contradiction

Back 57

a truth-functionally inconsistent statement. any formula whose truth table contains only F's under its main operator.

Front 58

contingent

Back 58

formulas which are true at seom lines of their truth tales and false at others are said to be truth-functionally contingent. this type of statement could be either true or false, so far as the logical operators are concerned.

NB: be careful with the semantics of propositional logic. if a statement is logically impossible, then it is inconsistent but may have a truth table that reveals it to be contingent.

Front 59

valid form

Back 59

an argument form every instances of which is valid. no situation where the premises are true and the conclusion is false.

Front 60

invalid form

Back 60

an argument form at least one instance of which is not valid. just takes one situation where the premises are true but the conclusion is false to make the argument invalid.

Front 61

To determine whether an argument from of propositional logic is valid

Back 61

put the entire form on a truth table, making as many lines as determined by the number of distinct sentence letters occurring in the relevant formulas.

If the table displays no counterexample, then the form is valid (and hence so is any instance of it). If the table displays one or more counterexamples, then the form is invalid

Front 62

Evaluate an argument

Back 62

1. determine whether all the premises are true.

2. determine whether the conclusion is at least probable, given the truth of the premises.

3. determine whether the premises are relevant to the conclusion.

4. determine whether the conclusion is vulnerable to new evidence.