I. SOME DEFINITIONS
• INFERENCE = one of the ways to get at a truth.o COHERENCE THEORY OF TRUTH
• INFERENCE ( wide sense ) = any procedure by which the head returns from one or more propositions to other propositions seen to be implied in the former.
• INFERENCE ( rigorous sense ) = the operation by which the head gets new cognition by pulling out the deductions of what is already known.
• INFERENCE = besides 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”
• N. B.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 non frailty versa ) .
2. The FALSITY of the CONSEQUENT involves the FALSITY of the ANTECEDENT ( but non frailty versa ) .
3. The connexion by virtuousness of which the consequent flows with LOGICAL NECESSITY from the ancestor is known as CONSEQUENCE or merely SEQUENCE.
4. The SEQUENCE ( which is signified by the so called CONCLUSION INDICATORS. e. g. . hence. accordingly. consequently. hence. therefore. and so. for this ground. etc ) is the VERY HEART of INFERENCE ; and when we make an illation. our assent bears on it straight.
• A GENUINE SEQUENCE is called VALID ; a PSEUDO SEQUENCE is called INVALID.
ANTECEDENT ( premises )
( connexion betweenINFERENCE the ancestor andthe consequent )
CONSEQUENT ( decision )
FORMAL AND MATERIAL VALIDITY
• FORMAL VALIDITY = the sequence springs from the signifier of illation o Example: Every S is a P ; hence some P is an S. O N. B. We can replace anything we want to for S and P. and the consequent will ever be true if the ancestor is true. o Example:
? S = Canis familiaris. P = animate being: Every Canis familiaris is an animate being ; therefore some animate being is a Canis familiaris. ? S = elector. P = citizen: Every elector is a citizen ; therefore some citizen is a elector.
• MATERIAL VALIDITY = the sequence springs from the particular character of the idea content. o Example: Every trigon is a plane figure bounded by three consecutive lines ; hence every plane figure bounded by three consecutive lines is a trigon. o Analysis:
? The illation is officially invalid for the consequent does non flux from the ancestor because of the signifier ; but materially valid because it does flux from the ancestor due to the particular character of the idea content. ? “Plane figure bounded by three consecutive lines” is a definition of “triangle” and is hence interchangeable.
Truth AND FORMAL VALIDITY
• LOGICAL TRUTH = consists in the conformance of our heads with world. o A proposition. as explained. is true if things are as the proposition says they are. • Logic surveies ground as an instrument for geting truth. and the attainment of truth must of all time stay the ultimate purpose of the logistician.
• N. B. We shall non be straight concerned with geting true informations but instead with conserving the truth of our informations as we draw illations from them. O In other words. we shall take at doing such a passage from informations to conclusion that if the information ( ancestor. premises ) are true. the decision ( consequent ) will needfully be true. O Formal cogency. rightness. uprightness. or consistence will be our immediate purpose. o We shall non inquire ourselves. ARE THE PREMISES TRUE? . but. DOES THE CONCLUSION FLOW FROM THE PREMISES so that IF the premises are true. the decision is needfully true? o The undermentioned syllogism is right in this proficient sense although the premises and the decision are false: ? No works is a life being ; but every adult male is a works ; hence no adult male is a life being. ? This syllogism is CORRECT FORMALLY.
• Why: because the decision truly flows from the premises by virtuousness of the signifier or construction of the statement. IF the premises were true. the decision would besides be true. o The undermentioned syllogism is non right officially although the premises and the decision are true: ? Every Canis familiaris is an animate being ; but no Canis familiaris is a works ; therefore no works is an animate being. ? The syllogism is non right because the decision does non truly flux from the premises. ? For case. we substitute “plant” with “cow” : • Every Canis familiaris is an animate being ; but no Canis familiaris is a cow ; hence no cow is an animate being.
IMMEDIATE AND MEDIATE INFERENCE
? IMMEDIATE INFERENCE = consists in go throughing straight ( that is. without the intermediacy of a in-between term or a 2nd proposition ) from one proposition to a new proposition that is a partial or complete reformulation of the really same truth expressed in the original proposition.
? MEDIATE INFERENCE = draws a decision from two propositions ( alternatively of one ) and does affect an progress in cognition. o It is mediate in either of two ways:? Categorical syllogism = it unites. or offprints. the topic and predicate of the decision through the intermediacy of a in-between term ; ? Conjectural syllogism = the major premiss “causes” the decision through the intermediacy of a 2nd proposition. o Goal: non merely a new proposition but besides a new truth ? There is an progress in cognition.
|SYNOPSIS | |IMMEDIATE INFERENCE |MEDIATE INFERENCE | |A. base on ballss from one proposition |A. base on ballss from two propositions | |B. without a medium |B. through a medium | |C. to a new proposition but non to a new truth |C. non merely to a new proposition but besides to a new truth |
DEDUCTION AND INDUCTION
• DEDUCTION = the procedure by which our heads proceed from a more cosmopolitan truth to a less cosmopolitan truth. o Example:? All work forces are mortal ; but Peter is a adult male ; hence Peter is mortal.
• INDUCTION = the procedure by which our heads proceed from sufficiently enumerated cases to a cosmopolitan truth. o Example:? This ruminant ( hoofed-mammal ) ( a cow ) is cloven-footed ; this one ( a cervid ) is cloven-footed ; and this one ( a caprine animal ) and this ( an antelope ) ; hence all ruminants are cloven-footed.
• Aristotelean Standpoint = cosmopolitan propositions about bing things imply the being of the things talked about.o Example:o All Stephen King’s novels are thrillers.• Implies the being of at least one novel by Stephen King. ? All unicorns are one-horned animate beings.• Does non connote the being of unicorns. • Boolean Standpoint = cosmopolitan propositions ne’er imply the being of the things talked about. ? All Stephen King’s novels are thrillers. • Does non connote the being of any novels by Stephen King. ? All unicorns are one-horned animate beings.
• Does non connote the being of unicorns. • Aristotelean and Boolean readings are the same for peculiar propositions. o Bot I and O propositions really claim that the capable category contains at least one bing thing. ? “Some” = at least one exists.
SQUARE OF OPPOSITION[ movie ]• CONTRADICTION = can non be true and false at the same clip • CONTRARY = At least 1of the propositions is false.• SUBCONTRARY = At least 1of the propositions is true. • SUBALTERNATION = truth flows down ; falseness flows up.
Bachhuber. Andrew H. . S. J. Introduction to Logic. New York: Appleton-Century-Crofts. Inc. . 1957.Sequence