Chapter 8 Flashcards
________ proposition combines two or more component propositions by means of a connective.
Compound propositions
Compound propositions that use the connective “or” are called ______ propositions.
disjunctive propositions
Compound propositions that use the connective if . .. then are called ______ propositions.
hypothetical
Categorical syllogism is a form of deductive reasoning and there are two types of non-categorical syllogisms that have:
Disjunctive and hypothetical propositions as premises
Name types of connectives that are used in compound propositions
“or” and “if….then”
The compound proposition that contains “or” is what type of proposition
disjunctive
The compound proposition that contains “if…. then” is what kind of proposition
hypothetical
Hypothetical propositions have the form “______” and they serve as premises in several types of inference.
If p, then q
An inference that uses “or” is the form of what kind of
syllogism?
Disjunctive
An antecedent in a hypothetical proposition is represented by which part of the “If p, then q” form?
“If X “ = antecedent
An consequent in a hypothetical proposition is represented by which part of the “If p, then q” form?
“then X “ = consequent
In the following hypothetical proposition which is the antecedent?
If it rains, then the graduation will be held in the gym
If it rains
In the following hypothetical proposition which is the consequent?
If it rains, then the graduation will be held in the gym
then the graduation will be held in the gym
In a ______ proposition, we are not actually asserting the truth of the antecedent or the consequent. We are saying that the truth of the first would be sufficient to guarantee the truth of the second. Until we know that it actually is raining, the possibility that the graduation will be held in the gym is merely ______. It is not something we can assert categorically.
hypothetical | hypothetical
Hypothetical propositions are used pervasively in ordinary speech to identify relationships of …..
dependence among facts , events, or possibilities.
______ are used pervasively in ordinary speech to identify relationships of dependence among facts , events, or possibilities.
Hypothetical propositions
Consider the statements:
- If I were president of the United States, I would be a politician.
- If I were a politician, I would be president of the United States.
These statements are examples of _____ propositions in which “if p, then q” is NOT equivalent to “if q, then p”
Hypothetical propositions
These are clearly not equivalent; 2 is true by definition (anyone who holds elective office must be a politician) , whereas 3 is dubious to say the least.
Hypothetical propositions are similar to that of “A” (universal, affirm) _______ propositions because the premise is not equivalent when the predicate and subject order is inverted.
categorical propositions
Another point of similarity between “A” categorical propositions and hypothetical propositions is that both have a valid ______. “All S are P” is equivalent to “All
non-P are non-S.” In the same way, “if p, then q” is equivalent to “if not-q, then not -p.”
For example:
4. If it rained last night , then the ground is wet this morning.
- If the ground is not wet this morning, then it did not rain last night.
These propositions are clearly equivalent, and it ‘s easy to see why the equivalence holds as a general rule.
contrapositive
The standard form of ________ propositions
is
If [antecedent], then [ consequent].
hypothetical
The antecedent and consequent are component
propositions that we represent by
lowercase letters : p, q, r, … not-p, not-q , not-r , …
The following are examples of what kind of form in a hypothetical statement/proposition:
p if q p only if q p if and only if q p unless q without X, q
Non-standard form
The following are examples of what kind of form in a hypothetical statement/proposition:
If q, then p If p, then q If q, then p and if p then q if not q, then p If X does not exist (occur), then q
Standard form
Syllogisms are
are types of arguments with two premises and a conclusion (so, three statements total)
There are three major types of syllogism:
categorical, disjunctive, and hypothetical syllogisms
If any argument (including any syllogism) is valid, then, when the argument’s premises are true, its conclusion must be _____.
true
________ syllogisms are useful in scientific reasoning, e.g., “either the cause of the sickness is factor A or factor B. It’s not A, so it is B.” When we rule out alternative explanation, we are reasoning by _______ syllogism.
Disjunctive
