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# Inductive and deductive reasoning

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### Inductive and deductive reasoning

1. 1. Inductive and deductiveInductive and deductive ReasoningReasoning PHIL200PHIL200
2. 2. Inductive and Deductive ArgumentsInductive and Deductive Arguments  Philosophy is centered in the analysis andPhilosophy is centered in the analysis and construction of arguments, which is calledconstruction of arguments, which is called logic.logic.  An argument is the supporting of a thesis (An argument is the supporting of a thesis ( the conclusion with reason (premises)the conclusion with reason (premises)  An argument consists of at least twoAn argument consists of at least two statements: a statement to be supported,statements: a statement to be supported, the conclusion and a statements thatthe conclusion and a statements that support it the conclusion.support it the conclusion.  This process of reasoning from premisesThis process of reasoning from premises to conclusion is known as inference.to conclusion is known as inference.
3. 3. Deductive and Inductive ReasoningDeductive and Inductive Reasoning  Arguments are two types-deductive andArguments are two types-deductive and inductive.inductive.  A deductive argument gives logicallyA deductive argument gives logically conclusive support to its conclusion.conclusive support to its conclusion.  An inductive argument gives probableAn inductive argument gives probable support to its conclusion.support to its conclusion.
4. 4. Inductive and Deductive ReasoningInductive and Deductive Reasoning  Arguments based on experience orArguments based on experience or observation are best expressed inductively,observation are best expressed inductively,  while arguments based on laws, rules, orwhile arguments based on laws, rules, or other widely accepted principles are bestother widely accepted principles are best expressed deductively.expressed deductively.
5. 5. DeductionDeduction  Deduction is the reasoning process thatDeduction is the reasoning process that draws a conclusion from the logicaldraws a conclusion from the logical relationship of two assertions, usually onerelationship of two assertions, usually one broad judgment or definition and one morebroad judgment or definition and one more specific assertion, often an inference.specific assertion, often an inference.
6. 6. Deductive ArgumentDeductive Argument  The two assertions that found the basis ofThe two assertions that found the basis of a deductive argument are called premises.a deductive argument are called premises.  The are usually two premises to consider:The are usually two premises to consider:  A major premise and a minor premise.A major premise and a minor premise. 1-Socrates is a Man1-Socrates is a Man 2-All men are Mortal2-All men are Mortal Therefore Socrates is MortalTherefore Socrates is Mortal
7. 7. Deductive ArgumentsDeductive Arguments  If Philosophy leads to wisdom, then it isIf Philosophy leads to wisdom, then it is worth studying.worth studying.  Philosophy leads to wisdomPhilosophy leads to wisdom Therefore Philosophy is worth studtying.Therefore Philosophy is worth studtying. If P then QIf P then Q PP Therefore QTherefore Q
8. 8. Deductive ArgumentsDeductive Arguments  A Deductive Argument that succeeds inA Deductive Argument that succeeds in providing logically conclusive support to itsproviding logically conclusive support to its conclusion is said to be valid, one that failsconclusion is said to be valid, one that fails is said to be invalid.is said to be invalid. 
9. 9. Deductive ArgumentDeductive Argument  If the two premises are constructedIf the two premises are constructed logically then the conclusion will alsologically then the conclusion will also follow logicallyfollow logically  We say that the deductive argument isWe say that the deductive argument is valid, this does not necessarily mean thatvalid, this does not necessarily mean that the conclusion is true or false,the conclusion is true or false,  Validity comes from a logical conclusionValidity comes from a logical conclusion based on logically constructed premises.based on logically constructed premises.
11. 11. Deductive ReasoningDeductive Reasoning  A deductive argument serves as the basisA deductive argument serves as the basis of an entire essay supporting theof an entire essay supporting the argument conclusion by supporting theargument conclusion by supporting the premises of the essay.premises of the essay.  In the previous example of Lincoln theIn the previous example of Lincoln the writer has to provide evidence that Lincolnwriter has to provide evidence that Lincoln actually performed with courage and aactually performed with courage and a clear purpose.clear purpose.
12. 12. Deductive ReasoningDeductive Reasoning  Note that the major premise of a deductiveNote that the major premise of a deductive argument is either a broad judgment or aargument is either a broad judgment or a definition.definition.  Thus, the major premise must beThus, the major premise must be supported based on values and beliefssupported based on values and beliefs that the writer expects the reader to share.that the writer expects the reader to share.  The minor premise is usually an inferenceThe minor premise is usually an inference about a particular person or situation,about a particular person or situation, supported by evidence as with inductivesupported by evidence as with inductive argument.argument.
13. 13. Examples of DeductionExamples of Deduction  Homosexuality is an immoral act, becauseHomosexuality is an immoral act, because it unnatural and is a contradiction to God’sit unnatural and is a contradiction to God’s law of procreation.law of procreation.  Major Premise: All acts that are unnaturalMajor Premise: All acts that are unnatural and contradict God Laws are immoral.and contradict God Laws are immoral.  Homosexuality contradicts God’s law ofHomosexuality contradicts God’s law of procreationprocreation  Homosexuality is immoral.Homosexuality is immoral.
14. 14. Deduction ExampleDeduction Example  Homosexuality is an immoral act, because itHomosexuality is an immoral act, because it unnatural and is a contradiction to God’s law ofunnatural and is a contradiction to God’s law of procreation. Thus, homosexuality should beprocreation. Thus, homosexuality should be banned.banned.  Major Premise: All acts that are unnatural andMajor Premise: All acts that are unnatural and contradict God’s Law are immoral and should becontradict God’s Law are immoral and should be banned.banned.  Homosexuality contradicts God’s law ofHomosexuality contradicts God’s law of procreationprocreation  Conclusion: Homosexuality is immoral andConclusion: Homosexuality is immoral and should be banned.should be banned.
15. 15. Reductio Ad AbsurdumReductio Ad Absurdum  An Indirect Method to prove or establish aAn Indirect Method to prove or establish a thesis.thesis.  You assume the opposite of what youYou assume the opposite of what you want to prove and then show that itwant to prove and then show that it produces a false conclusion. Thereforeproduces a false conclusion. Therefore your thesis must be true.your thesis must be true.  See Page 33See Page 33  ..
16. 16. Inductive ArgumentsInductive Arguments  Inductive Arguments are not truth preserving. AnInductive Arguments are not truth preserving. An inductive argument cannot prove if the premisesinductive argument cannot prove if the premises are true then the conclusion will also be true. Itare true then the conclusion will also be true. It is intended to prove only probable support to theis intended to prove only probable support to the conclusion.conclusion.  An inductive argument that succeeds inAn inductive argument that succeeds in providing such probable support is said to beproviding such probable support is said to be strong. An inductive argument that fails tostrong. An inductive argument that fails to provide such support is said to be weak. Aprovide such support is said to be weak. A strong argument with true premises is said to bestrong argument with true premises is said to be cogent.cogent.  Page 34Page 34
17. 17. Enumerative InductionEnumerative Induction  A common inductive argument form reasons fromA common inductive argument form reasons from premises about a few members of the group topremises about a few members of the group to conclusions about the group as a whole.( example pageconclusions about the group as a whole.( example page 35)35)  The group generalized is theThe group generalized is the target grouptarget group..  The observed or the known members of the group areThe observed or the known members of the group are called thecalled the samplesample..  To reach a reliable conclusion about the target group theTo reach a reliable conclusion about the target group the sample should be large enough and representative ofsample should be large enough and representative of the whole group.the whole group.  Drawing conclusions about a target group based on aDrawing conclusions about a target group based on a sample that is too small is a common error known assample that is too small is a common error known as hasty generalization.hasty generalization.
18. 18. Inference to the Best ExplanationInference to the Best Explanation ( abduction)( abduction)  A Type of inductive reasoning.A Type of inductive reasoning.  We reason from premises about a state ofWe reason from premises about a state of affairs to reach a conclusion about a state ofaffairs to reach a conclusion about a state of affairs. ( page 36)affairs. ( page 36)  Inference to the Best explanation is especiallyInference to the Best explanation is especially important in science, where scientists advanceimportant in science, where scientists advance their theories or hypothesis to explain a set oftheir theories or hypothesis to explain a set of data, then evaluating these explanations to seedata, then evaluating these explanations to see what is best.what is best.  The theory of planetary movementsThe theory of planetary movements ( heliocentric ( sun-centered theory) as an( heliocentric ( sun-centered theory) as an alternative to earth centered (Ptolemaic view)alternative to earth centered (Ptolemaic view)
19. 19. Fallacies of ReasoningFallacies of Reasoning  Ad HominemAd Hominem  This argument attacks the person instead of his positionThis argument attacks the person instead of his position Example:Example:  What she says about Johannes Kepler’s astronomy of theWhat she says about Johannes Kepler’s astronomy of the 1600′s must be just so much garbage. Do you realize she’s only1600′s must be just so much garbage. Do you realize she’s only fourteen years old?fourteen years old?  This attack may undermine the arguer’s credibility as aThis attack may undermine the arguer’s credibility as a scientific authority, but it does not undermine herscientific authority, but it does not undermine her reasoning.reasoning.  That reasoning should stand or fall on the scientificThat reasoning should stand or fall on the scientific evidence, not on the arguer’s age or anything else aboutevidence, not on the arguer’s age or anything else about her personally.her personally.
20. 20. Argument from AuthorityArgument from Authority  This argument appeals to authoritativeThis argument appeals to authoritative figure as means of persuation.figure as means of persuation.  You should believe in the death penaltyYou should believe in the death penalty because Plato believed in itbecause Plato believed in it
21. 21. Arguing in CirclesArguing in Circles  Begging the QuestionBegging the Question  A form of circular reasoning in which a conclusion isA form of circular reasoning in which a conclusion is derived from premises that presuppose the conclusion.derived from premises that presuppose the conclusion.  Normally, the point of good reasoning is to start out atNormally, the point of good reasoning is to start out at one place and end up somewhere new, namely havingone place and end up somewhere new, namely having reached the goal of increasing the degree of reasonablereached the goal of increasing the degree of reasonable belief in the conclusion.belief in the conclusion.  The point is to make progress, but in cases of beggingThe point is to make progress, but in cases of begging the question there is no progress.the question there is no progress.  Example:Example:  See Example page 39See Example page 39
22. 22. Appeal to IgnoranceAppeal to Ignorance The fallacy of appeal to ignorance comes in two forms:The fallacy of appeal to ignorance comes in two forms:  (1) Not knowing that a certain statement is true is taken to be a proof that it is(1) Not knowing that a certain statement is true is taken to be a proof that it is false.false.  (2) Not knowing that a statement is false is taken to be a proof that it is true.(2) Not knowing that a statement is false is taken to be a proof that it is true.  The fallacy uses an unjustified attempt to shift the burden of proof. TheThe fallacy uses an unjustified attempt to shift the burden of proof. The fallacy is also called “Argument from Ignorance.”fallacy is also called “Argument from Ignorance.”  Example:Example:  Nobody has ever proved to me there’s a God, so I know there is no God.Nobody has ever proved to me there’s a God, so I know there is no God.  This kind of reasoning is generally fallacious. It would be proper reasoningThis kind of reasoning is generally fallacious. It would be proper reasoning only if the proof attempts were quite thorough, and it were the case that ifonly if the proof attempts were quite thorough, and it were the case that if God did exist, then there would be a discoverable proof of this.God did exist, then there would be a discoverable proof of this.