Philosophy quiz 9
Standard form
A categorical syllogism is in standard form when the premise containing the major term is on top; the minor term in premise 2; and the conclusion last with a line separating it from the premises.
Compound propositions
Composed of 2 or more categorical propositions. The 2 fundamental compound propositions are disjunctive and conditional.
Logically simple proposition
Composed of a single subject and predicate. Categorical propositions are simple in this sense.
Conditional/hypothetical proposition
Compound proposition where 2 categorical propositions are connected with "if..., then..." By themselves, they only assert that there's a relation (usually between cause and effect) between the antecedent and the consequent. Conditional propositions don't assert that either the antecedent or consequent is true. They assert that if the antecedent is true, then the consequent must also be true. EX: "If it rains tomorrow, then my house will get wet." The 2 categorical propositions are: "Tomorrow it rains" and "Tomorrow my house gets wet."
Categorical syllogism (deductive)
Deductive argument with 2 categorical premises and a categorical conclusion. EX: All humans are mortal Socrates is a human Socrates is mortal.
Disjunctive syllogism
Deductive arguments with one categorical premise and one disjunctive proposition (understood in the weak "or" sense).
Conditional/hypothetical syllogisms
Deductive arguments with one or more conditional propositions.
Statements
Either true or false; only deductive arguments are valid or invalid.
Antecedent
Former term ("it rains tomorrow"). EX: "If it rains tomorrow, then my house will get wet."
Or
It's important to note the ambiguity of "or." When a waitperson says that you may have either soup or salad with your dinner, they usually mean that you may have one or the other (strong) but not both. In other cases, "or" simply means "at least one" (weak). Only context and common sense allows us to determine which sense is intended when 2 propositions are jointed with an "or." When much hinges on making sure there are no misunderstandings, (in legal documents), it's conventional to use "and/or" when one intends to assert that at least one of the disjuncts is true. From a purely logical point of view, it's best to assume that "or" means "at least one" unless context makes it obvious that the strong "or" is intended.
Disjunctive propositions
Joins 2 (or more) categorical propositions - (1) It will rain and (2) It will snow - with "or." The disjunctive proposition becomes: "Either it will rain or it will snow."
Consequent
Latter term ("my house will get wet"). EX: "If it rains tomorrow, then my house will get wet."
Sound deductive argument
One with both valid form and true content.
Validity
Property of deductive arguments. Refers to the form of an argument, not its content. In the strict sense in which the term is used in a logic class, it makes no sense to speak of a statement as being either valid or invalid. In the everyday world we tend to use "valid" to mean "true" or even "I agree with you." It's important in logic to keep the distinction between the word "valid" - which applies only to certain forms of deductive arguments and the word "true" -which applies to propositions (statements or claims - sentences that have a truth value). In this course, to say that a statement is valid is as nonsensical as saying that the concept 7 is blue.
Invalid
Since the counter-example has true premises and a false conclusion it's invalid. Since it has the same form as the argument for the roundness of the earth, that argument must be invalid too. The fact that the earth is round and that we do in fact see the tops of ships before we see their bottom doesn't mean that the argument is valid; it only means that it happens (by accident) to have true content. It's possible to get the correct answer to a math problem even though the reasoning is in error.
Counter-examples EX: A
Suppose someone argues that we can deductively prove that the earth is round: If the earth is round, then we should see the top of a ship sailing into port before we see its bottom. In point of fact, we do see the tops of ships before we can see their bottom. Therefore, the earth must be round. First, abstract the form(left). Second, we produce the counter-example: If George Washington is beheaded, then he'd be dead. George Washington is dead. Therefore, George Washington was beheaded. The form of the 2nd argument is (same form as the earth argument) (right).
Hypothetical chains (hypothetical syllogism)
The chain in a hypothetical chain can be more than 2 premises long.
Deductive argument (justification)
The conclusion follows with logical necessity from the premises. If the premises (content) are true and the inference (form) valid, then it's logically impossible that the conclusion be false. The form of a deductive argument may be valid, even if all its content is false. An argument may be invalid, even if all its content is true.
Figure
The figure of a standard form categorical syllogism refers to the location of the middle term.
Mood
The mood of a standard form categorical syllogism is the letter designation (A, E, I, O) of each statement read from top to bottom.
Major term
The predicate term of the conclusion in a categorical syllogism.
Minor term
The subject term of the conclusion in a categorical syllogism.
Middle term
The term that only appears in the premises.
Counter-examples
Useful tool for evaluating arguments of all kinds. 2 steps in a refutation by counter example: 1) Abstract the form of the argument in question. 2) Construct a 2nd argument that has the same form as the one in question with premises that are obviously true and a conclusion that is obviously false. Since valid means it's logically impossible that the premises be true and the conclusion false, this 2nd argument will have a form which is invalid. Since this 2nd argument was constructed in such a way that it has the same form as the argument in question, the form of the questionable argument must also be invalid even if all its premises and its conclusion are true.