Deductive Reasoning Previously we noted that there are two basic categories of reasoning namely deductive and inductive Over the next two weeks well look at each of these categories in turn beginning with deductive reasoningTo recapitulate the main points already mentioned about deductive reasoningDeductive reasoning is based on deductive inference If one statement C strictly or logically follows from a set of statements eg consisting of A and Bthen C is said to be deduced from A and BWe say that we can infer deductively C from A and BA way of understanding the strict or logical nature of deductive inference is to understand it as mechanical The inference in this sense can be calculated and as such it can be done by machine just as we calculate in arithmeticSo long as a machine works the rules designed into it ie the ways its procedures are designed to be executed will invariably be followed Lets look at an example of deductive inferenceWe know lets say that if Gary has the money then he buys a canoe In other words we deny the possibility of Gary having the money but not buying a canoe Also we know that Gary does indeed have the money From these two premisses we can infer that Gary buys the canoe This inference is strict in the sense that if we accept the two premisses as true we are rationally obligated to accept the conclusion as true To deny that Gary buys a canoe while accepting the premisses is irrationalin order to do this one would have to give up on following the basic rules of logic that underpin our reasoning The rule of logic followed in the argument above is known as affirming the antecedent or modus ponens Lets look at this again and then well go on to consider other such rulesThe first premiss of our argument is called a conditional statement It says If Gary has the money then Gary buys a canoe The conditional is sometimes therefore known as an ifthen statementAll conditionals have both an ifclause Gary has the money in this case and a thenclause Gary buys a canoe These are otherwise known as the antecedent and consequent respectively The argument takes the form of affirming the antecedent that is after stating the conditional is true we state that the conditionals antecedent is true And from the truth of these two statements it follows that the consequent is true ie Gary buys the canoe This last statement is of course the arguments conclusionWhy must the consequent be true in this case Well we said that the conditional if Gary has the money then he buys a canoe aims to deny that the antecedent can be true and the consequent false ie that Gary has the money but he doesnt buy a canoe In other words the conditional is true so long as it is not the case that Gary has the money and doesnt buy a canoe Hence if we know that the conditional is true and that the antecedent is

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