Inductive and deductive reasoning

Inductive and deductiveInductive and deductive
ReasoningReasoning
PHIL200PHIL200

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.

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.

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.

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.

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

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

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.


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.

Constructing a Deductive ArgumentConstructing a Deductive Argument
 When constructing a deductive argument,When constructing a deductive argument,
your task is to defend the truth of youryour task is to defend the truth of your
premises.premises.
 If your argument is valid, i.e., logicallyIf your argument is valid, i.e., logically
constructed, then the reader must agreeconstructed, then the reader must agree
with your argument.with your argument.
 If the reader disagrees, then the readerIf the reader disagrees, then the reader
must prove that one of the premises is notmust prove that one of the premises is not
true.true.

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.

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.

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.

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.

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
 ..

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

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.

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)

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.

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

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

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.”
 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.

False DilemmaFalse Dilemma
 Unfairly presenting too few choices and then implying that a choiceUnfairly presenting too few choices and then implying that a choice
must be made among this short menu of choices commits the falsemust be made among this short menu of choices commits the false
dilemma fallacy.dilemma fallacy.
 I want to go to Scotland from London. I overheard McTaggart sayI want to go to Scotland from London. I overheard McTaggart say
there are two roads to Scotland from London: the high road and thethere are two roads to Scotland from London: the high road and the
low road. I expect the high road would be too risky because it’slow road. I expect the high road would be too risky because it’s
through the hills and that means dangerous curves. But it’s rainingthrough the hills and that means dangerous curves. But it’s raining
now, so both roads are probably slippery. I don’t like either choice,now, so both roads are probably slippery. I don’t like either choice,
but I guess I should take the low road and be safer.but I guess I should take the low road and be safer.
 This would be fine reasoning is you were limited to only two roads,This would be fine reasoning is you were limited to only two roads,
but you’ve falsely gotten yourself into a dilemma with suchbut you’ve falsely gotten yourself into a dilemma with such
reasoning. There are many other ways to get to Scotland.reasoning. There are many other ways to get to Scotland.

Slippery Slop ArgumentSlippery Slop Argument
 This fallacy consists of arguing without good reasons, that taking a particular step willThis fallacy consists of arguing without good reasons, that taking a particular step will
inevitably lead to another, normally catastrophic steps.inevitably lead to another, normally catastrophic steps.
 Mom: Those look like bags under your eyes. Are you getting enough sleep?Mom: Those look like bags under your eyes. Are you getting enough sleep?
 Jeff: I had a test and stayed up late studying.Jeff: I had a test and stayed up late studying.
 Mom: You didn’t take any drugs, did you?Mom: You didn’t take any drugs, did you?
 Jeff: Just caffeine in my coffee, like I always do.Jeff: Just caffeine in my coffee, like I always do.
 Mom: Jeff! You know what happens when people take drugs! Pretty soon the caffeineMom: Jeff! You know what happens when people take drugs! Pretty soon the caffeine
won’t be strong enough. Then you will take something stronger, maybe someone’swon’t be strong enough. Then you will take something stronger, maybe someone’s
diet pill. Then, something even stronger. Eventually, you will be doing cocaine. Thendiet pill. Then, something even stronger. Eventually, you will be doing cocaine. Then
you will be a crack addict! So, don’t drink that coffee.you will be a crack addict! So, don’t drink that coffee.

Straw ManStraw Man
 You commit the straw man fallacy whenever you attribute an easilyYou commit the straw man fallacy whenever you attribute an easily
refuted position to your opponent, one that the opponent wouldn’trefuted position to your opponent, one that the opponent wouldn’t
endorse, and then proceed to attack the easily refuted position (theendorse, and then proceed to attack the easily refuted position (the
straw man) believing you have undermined the opponent’s actualstraw man) believing you have undermined the opponent’s actual
position. Example (a debate before the city council):position. Example (a debate before the city council):
 Opponent: Because of the killing and suffering of Indians thatOpponent: Because of the killing and suffering of Indians that
followed Columbus’s discovery of America, the City of Berkeleyfollowed Columbus’s discovery of America, the City of Berkeley
should declare that Columbus Day will no longer be observed in ourshould declare that Columbus Day will no longer be observed in our
city.city.
 Speaker: This is ridiculous, fellow members of the city council. It’s notSpeaker: This is ridiculous, fellow members of the city council. It’s not
true that everybody who ever came to America from another countrytrue that everybody who ever came to America from another country
somehow oppressed the Indians. I say we should continue to observesomehow oppressed the Indians. I say we should continue to observe
Columbus Day, and vote down this resolution that will make the CityColumbus Day, and vote down this resolution that will make the City
of Berkeley the laughing stock of the nation.of Berkeley the laughing stock of the nation.
 The speaker has twisted what his opponent said; the opponent neverThe speaker has twisted what his opponent said; the opponent never
said, nor even indirectly suggested, that everybody who ever came tosaid, nor even indirectly suggested, that everybody who ever came to
America from another country somehow oppressed the Indians.America from another country somehow oppressed the Indians.

Genetic FallacyGenetic Fallacy
 A critic commits the genetic fallacy if the criticA critic commits the genetic fallacy if the critic
attempts to discredit or support a claim or anattempts to discredit or support a claim or an
argument because of its origin (genesis) whenargument because of its origin (genesis) when
such an appeal to origins is irrelevant.such an appeal to origins is irrelevant.
 Whatever your reasons are for buying that DVDWhatever your reasons are for buying that DVD
they’ve got to be ridiculous. You said yourself that youthey’ve got to be ridiculous. You said yourself that you
got the idea for buying it from last night’s fortunegot the idea for buying it from last night’s fortune
cookie. Cookies can’t think!cookie. Cookies can’t think!

Fallacies of CompositionFallacies of Composition
 The composition fallacy occurs when someoneThe composition fallacy occurs when someone
mistakenly assumes that a characteristic ofmistakenly assumes that a characteristic of
some or all the individuals in a group is also asome or all the individuals in a group is also a
characteristic of the group itself, the groupcharacteristic of the group itself, the group
“composed” of those members. It is the“composed” of those members. It is the
converse of the division fallacy.converse of the division fallacy.
 Each human cell is very lightweight, so a humanEach human cell is very lightweight, so a human
being composed of cells is also very lightweight.being composed of cells is also very lightweight.

InconsistencyInconsistency
 The fallacy occurs when we accept an inconsistent set ofThe fallacy occurs when we accept an inconsistent set of
claims, that is, when we accept a claim that logicallyclaims, that is, when we accept a claim that logically
conflicts with other claims we hold.conflicts with other claims we hold.
 I’m not racist. Some of my best friends are white. But II’m not racist. Some of my best friends are white. But I
just don’t think that white women love their babies asjust don’t think that white women love their babies as
much as our women do.much as our women do.
 That last remark implies the speaker is a racist, althoughThat last remark implies the speaker is a racist, although
the speaker doesn’t notice the inconsistency.the speaker doesn’t notice the inconsistency.

Inductive and deductive reasoning

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Inductive and deductive reasoning