Terms in this set (9)

An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

The logical process of passing from observations and axioms to generalizations; in statistics, the development of generalizations from sample data, usually with calculated degrees of uncertainty.

Scientists make inferences about how and why things work based on their investigations and observations. Inferences are formed from what is observed combined with the observer’s experience and knowledge. As a scientist learns and observes more, their inferences may change.

There are two types of inferences, inductive and deductive. Inductive inferences start with an observation and expand into a general conclusion or theory.

• Modus Ponens (M.P.) -If P then Q. -P.
• Modus Tollens (M.T.) -If P then Q.
• Hypothetical Syllogism (H.S.) -If P then Q.
• Disjunctive Syllogism (D.S.) -P or Q.
• Conjunction (Conj.) -P.
• Constructive Dilemma (C.D.) -(If P then Q) and (If R then S)
• Simplification (Simp.) -P and Q.
• Absorption (Abs.) -If P then Q.

In addition to conversion (and subalternation), there are two other types of immediate inferences that traditional logic addresses: obversion and contraposition….Obversion.

Obversion

An immediate inference is an inference which can be made from only one statement or proposition. For instance, from the statement “All toads are green”, the immediate inference can be made that “no toads are not green”.

The clearest cases of immediate inference are demonstrated by the Square of Opposition. For example, if we know the definition of contrary propositions, if we know the truth value of a Universal Affirmative proposition we can immediately infer the truth value of its contrary.

The type of inference exhibited here is called abduction or, somewhat more commonly nowadays, Inference to the Best Explanation.

• 1.1 Deduction, induction, abduction. Abduction is normally thought of as being one of three major types of inference, the other two being deduction and induction.
• 1.2 The ubiquity of abduction.

Immediate argument: An argument that has only one premise. Mediate argument: An argument that has more than one premise. Conversion: An immediate argument created by interchanging the subject and predicate terms of a given categorical proposition.

Two statements are subcontrary if they are both particular statements that differ in quality. Subcontraries may at the same time both be true, but cannot at the same time both be false. If “Some men are mortal” is false, then “Some men are not mortal cannot be false . differ in quantity.

: the relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of “If it rains, then they cancel school” is “If they do not cancel school, then it does not rain.”

The converse of p → q is q → p. The inverse of p → q is ∼ p →∼ q. A conditional statement and its converse are NOT logically equivalent. A conditional statement and its inverse are NOT logically equivalent.

: a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them “if not-B then not-A ” is the contrapositive of “if A then B “

To prove a conjecture is true, you must prove it true for all cases. It only takes ONE false example to show that a conjecture is NOT true. This false example is a COUNTEREXAMPLE. Find a counterexample to show that each conjecture is false.

1a : the action or logical operation of negating or making negative. b : a negative statement, judgment, or doctrine especially : a logical proposition formed by asserting the falsity of a given proposition — see Truth Table. 2a : something that is the absence of something actual : nonentity.