GENERAL NOTION OF INFERENCE
I. SOME DEFINITIONS
• INFERENCE = one of the ways to arrive at a truth.
o COHERENCE THEORY OF TRUTH
• INFERENCE (broad sense) = any process by which the mind proceeds from one or more propositions to other propositions seen to be implied in the former.
• INFERENCE (strict sense) = the operation by which the mind gets new knowledge by drawing out the implications of what is already known.
• INFERENCE = also applied to any series of propositions so arranged that one, called the CONSEQUENT, flows with logical necessity from one or more others, called the ANTECEDENT.
• ANTECEDENT (Latin, antecedo) = “that which goes before” o Defined as “that from which something is inferred”
• CONSEQUENT ( Latin, consequor) = “that which follows after” o Defined as “that which is inferred from the antecedent”
1. The ANTECEDENT AND CONSEQUENT of a VALID INFERENCE are so related that the TRUTH of the ANTECEDENT involves the TRUTH of the CONSEQUENT (but not vice versa).
2. The FALSITY of the CONSEQUENT involves the FALSITY of the ANTECEDENT (but not vice versa).
3. The connection by virtue of which the consequent flows with LOGICAL NECESSITY from the antecedent is known as CONSEQUENCE or simply SEQUENCE.
4. The SEQUENCE (which is signified by the so called CONCLUSION INDICATORS, e.g., therefore, consequently, accordingly, hence, thus, and so, for this reason, etc) is the VERY HEART of INFERENCE; and when we make an inference, our assent bears on it directly.
• A GENUINE SEQUENCE is called VALID; a PSEUDO SEQUENCE is called INVALID.
INFERENCE the antecedent and
FORMAL AND MATERIAL VALIDITY
• FORMAL VALIDITY = the sequence springs from the form of inference o Example: Every S is a P; therefore some P is an S. o N.B. We can substitute anything we want to for S and P, and the consequent will always be true if the antecedent is true. o Example:
▪ S = dog, P = animal: Every dog is an animal; therefore some animal is a dog. ▪ S = voter, P = citizen: Every voter is a citizen; therefore some citizen is a voter.
• MATERIAL VALIDITY = the sequence springs from the special character of the thought content. o Example: Every triangle is a plane figure bounded by three straight lines; therefore every plane figure bounded by three straight lines is a triangle. o Analysis:
▪ The inference is formally invalid for the consequent does not flow from the antecedent because of the form; but materially valid because it does flow from the antecedent due to the special character of the thought content. ▪ “Plane figure bounded by three straight lines” is a definition of “triangle” and is therefore interchangeable.
TRUTH AND FORMAL VALIDITY
• LOGICAL TRUTH = consists in the conformity of our minds with reality. o A proposition, as explained, is true if things are as the proposition says they are. • Logic studies reason as an instrument for acquiring truth, and the attainment of truth must ever remain the ultimate aim of the logician.
• N.B. We shall not be directly concerned with acquiring true data but rather with conserving the truth of our data as we draw inferences from them. o In other words, we shall aim at making such a transition from data to conclusion that if the data (antecedent, premises) are true, the conclusion (consequent) will necessarily be true. o Formal validity, correctness, rectitude, or consistency will be our immediate aim. o We shall not ask ourselves, ARE THE PREMISES...