5/1/09 Under construction
argument:
a conclusion, together with zero or more premises which are intended to support it.
conclusion:
a true or false statement
deductive (argument):
an argument in which the premises are intended to conclusively establish the conclusion; valid deductive arguments achieve this, invalid deductive arguments fall short of this ideal
inductive (argument):
an argument in which the premises are intended to constitute some sort of support for the conclusion, while not necessarily aiming at conclusive support. Traditionally, arguments of the form 'some->all' , for example 'some swans are white, therefore all swans are white' are the central examples of inductive arguments. But often other less than conclusive types of argument, for example 'most swans are white, therefore any swans to be found in the botanical gardens will be white' are also classified as being inductive.
invalid (argument):
an argument in which it is possible for all the premises to be true and the conclusion false at one and the same time (ie the truth of the premises does not conclusively establish the truth of the conclusion)
premise:
a true or false statement
statement:
roughly, a true or false indicative sentence. (Terms like 'statement', 'sentence', 'proposition' are terms of art within logic. Partly this is because logic has need to accomodate the facts that the same things can be said in different ways or even in different languages. Getting in too deep here does not suit the purposes of an elementary logic course, so we use these terms loosely and interchangeably.)
valid (deductive argument):
an argument in which it is not possible for all the premises to be true and the conclusion false at one and the same time. The truth of the premises guarantees the truth of the conclusion.
valid (inductive argument):
is a nonsense expression. Some philosophers and logicians wish to use the word 'valid' of some inductive arguments. They reason as follows. The words 'valid' and 'invalid' are honorifics (ie praise or blame). Some deductive arguments are valid (ie good) and others invalid (ie bad). But also some inductive arguments are good inductive arguments (while others are bad inductive arguments). Why can't we call those good inductive arguments 'valid inductive arguments'? The answer to this is. The words 'valid' and 'invalid' are not merely praise and blame. Rather they indicate the presence or absence of a certain property, namely the property that the truth of the premises guarantees the truth of the conclusion. No inductive argument has this property. So all inductive arguments are invalid, period.
atomic proposition
a single indivisible proposition which has no other proposition as a component part
bi-implication
is a type of compound proposition which, in our system, has its main connective symbolized by ≡ . In English, this main connective typically appears as 'if and only if'.
compound proposition
a proposition which has one or more other propositions as component parts
conjunction
is a type of compound proposition which, in our system, has its main connective symbolized by ∧. In English, this main connective typically appears as 'and'.
disjunction
is a type of compound proposition which, in our system, has its main connective symbolized by ∨ . In English, this main connective typically appears as 'or
implication
is a type of compound proposition which, in our system, has its main connective symbolized by ⊃ . In English, this main connective typically appears as 'if .. then'.
main connective
every compound proposition has exactly one main connective. Every compound proposition is either a conjunction, disjunction, negation, etc., and has the appropriate symbol as its main connective. In turn, the component propositions of a compound proposition are either atomic or are themselves compound propositions with their own main connectives.
negation
is a type of compound proposition which, in our system, has its main connective symbolized by ∼ . In English, this main connective typically appears as 'not'.
argument:
a conclusion, together with zero or more premises which are intended to support it.
atomic proposition
a single indivisible proposition which has no other proposition as a component part.
bi-implication
is a type of compound proposition which, in our system, has its main connective symbolized by ≡ . In English, this main connective typically appears as 'if and only if'.
compound proposition
a proposition which has one or more other propositions as component parts.
conclusion:
a true or false statement
conjunction
is a type of compound proposition which, in our system, has its main connective symbolized by ∧. In English, this main connective typically appears as 'and'.
disjunction
is a type of compound proposition which, in our system, has its main connective symbolized by ∨ . In English, this main connective typically appears as 'or
deductive (argument):
an argument in which the premises are intended to conclusively establish the conclusion; valid deductive arguments achieve this, invalid deductive arguments fall short of this ideal
inductive (argument):
an argument in which the premises are intended to constitute some sort of support for the conclusion, while not necessarily aiming at conclusive support. Traditionally, arguments of the form 'some->all' , for example 'some swans are white, therefore all swans are white' are the central examples of inductive arguments. But often other less than conclusive types of argument, for example 'most swans are white, therefore any swans to be found in the botanical gardens will be white' are also classified as being inductive.
implication
is a type of compound proposition which, in our system, has its main connective symbolized by ⊃ . In English, this main connective typically appears as 'if .. then'.
invalid (argument):
an argument in which it is possible for all the premises to be true and the conclusion false at one and the same time (ie the truth of the premises does not conclusively establish the truth of the conclusion)
main connective
every compound proposition has exactly one main connective. Every compound proposition is either a conjunction, disjunction, negation, etc., and has the appropriate symbol as its main connective. In turn, the component propositions of a compound proposition are either atomic or are themselves compound propositions with their own main connectives.
negation
is a type of compound proposition which, in our system, has its main connective symbolized by ∼ . In English, this main connective typically appears as 'not'.
premise:
a true or false statement
statement:
roughly, a true or false indicative sentence. (Terms like 'statement', 'sentence', 'proposition' are terms of art within logic. Partly this is because logic has need to accomodate the facts that the same things can be said in different ways or even in different languages. Getting in too deep here does not suit the purposes of an elementary logic course, so we use these terms loosely and interchangeably.)
valid (deductive argument):
an argument in which it is not possible for all the premises to be true and the conclusion false at one and the same time. The truth of the premises guarantees the truth of the conclusion.
valid (inductive argument):
is a nonsense expression. Some philosophers and logicians wish to use the word 'valid' of some inductive arguments. They reason as follows. The words 'valid' and 'invalid' are honorifics (ie praise or blame). Some deductive arguments are valid (ie good) and others invalid (ie bad). But also some inductive arguments are good inductive arguments (while others are bad inductive arguments). Why can't we call those good inductive arguments 'valid inductive arguments'? The answer to this is. The words 'valid' and 'invalid' are not merely praise and blame. Rather they indicate the presence or absence of a certain property, namely the property that the truth of the premises guarantees the truth of the conclusion. No inductive argument has this property. So all inductive arguments are invalid, period.