Logic in School Logic in School ProgramProgram

Creighton UniversityCreighton University

Director: Dr. Jinmei Yuan (Director: Dr. Jinmei Yuan (jinmei@creighton.edujinmei@creighton.edu)) Student Teachers: Mark HolmbergStudent Teachers: Mark Holmberg

Andrew Trapp Andrew Trapp Jason Bodewitz Jason Bodewitz Elizabeth Epsen Elizabeth Epsen

http://www.youtube.com/watch?v=xrShK-NVhttp://www.youtube.com/watch?v=xrShK-NVMIUMIU

OverviewOverview

Meet every weekMeet every week There will be quizzes (about every There will be quizzes (about every

2 weeks at the beginning of 2 weeks at the beginning of class), some homework class), some homework assignments, tests, and in-class assignments, tests, and in-class handouts/exerciseshandouts/exercises– The quizzes could be unannouncedThe quizzes could be unannounced– We will tell you the test dates in We will tell you the test dates in

advanceadvance

Overview Part IIOverview Part II

Typical schedule each day:Typical schedule each day:– Journal exerciseJournal exercise– Go over questions from Go over questions from

homework/previous class lesson (if homework/previous class lesson (if any)any)

– LessonLesson– Example problems / questionsExample problems / questions– Assign homework problems / readingsAssign homework problems / readings

Class NotesClass Notes

Please raise your hand if you have a Please raise your hand if you have a question or wish to answer one of question or wish to answer one of oursours

We want to encourage everyone to We want to encourage everyone to get involved in class, so even if get involved in class, so even if you’re not sure of an answer for you’re not sure of an answer for instance, still feel free to try to instance, still feel free to try to answer – we are all learning together answer – we are all learning together

Lesson 1: Basic ConceptsLesson 1: Basic ConceptsArguments, Premises, and Arguments, Premises, and

ConclusionsConclusions LogicLogic: the organized body of knowledge, : the organized body of knowledge,

or science, that evaluates argumentsor science, that evaluates arguments– Aim: to develop system of methods to use as Aim: to develop system of methods to use as

criteria for evaluating arguments of others criteria for evaluating arguments of others and for constructing our own; to determine and for constructing our own; to determine good arguments from bad argumentsgood arguments from bad arguments

Syllogistic logicSyllogistic logic: developed by Aristotle (384-322 : developed by Aristotle (384-322 B.C.); a kind of logic in which the fundamental B.C.); a kind of logic in which the fundamental elements are elements are termsterms, and arguments are evaluated , and arguments are evaluated as good or bad depending on how the terms are as good or bad depending on how the terms are arranged in the argumentarranged in the argument

Modal logicModal logic: also by Aristotle, but includes : also by Aristotle, but includes concepts such as possibility, necessity, belief, and concepts such as possibility, necessity, belief, and doubtdoubt

ArgumentsArguments

ArgumentArgument: a group of statements, : a group of statements, one or more of which (premises) one or more of which (premises) are claimed to provide support for, are claimed to provide support for, or reasons to believe, one of the or reasons to believe, one of the others (conclusions)others (conclusions)– Good argument: premises support the Good argument: premises support the

conclusionconclusion– Bad argument: premises do not Bad argument: premises do not

support conclusion (even if they claim support conclusion (even if they claim to)to)

ArgumentsArguments

Made up of statementsMade up of statements– Statement: a sentence that is either true Statement: a sentence that is either true

(T) or false (⊥) (T) or false (⊥) Melatonin helps relieve jet lag. (T)Melatonin helps relieve jet lag. (T) No wives ever cheat on their husbands. (⊥)No wives ever cheat on their husbands. (⊥)

Truth values (of a statement)Truth values (of a statement) Many sentences, unlike statements, Many sentences, unlike statements,

cannot be said to be T or ⊥cannot be said to be T or ⊥– Questions (Where is Tom?)Questions (Where is Tom?)– Proposals (Let’s go to a movie.)Proposals (Let’s go to a movie.)– Suggestions (I suggest you get contact Suggestions (I suggest you get contact

lenses.)lenses.)– Commands (Turn off the TV.)Commands (Turn off the TV.)– Exclamations (Wow!)Exclamations (Wow!)

StatementsStatements

1.1. PremisesPremises• Statements that set forth the Statements that set forth the

reasons or evidencereasons or evidence

2.2. ConclusionsConclusions• Statements that the evidence is Statements that the evidence is

claimed to support or imply claimed to support or imply (claimed to follow from the (claimed to follow from the premises)premises)

Example of an Example of an ArgumentArgument

Good Argument:Good Argument:1.1. All film stars are celebrities. (Premise 1)All film stars are celebrities. (Premise 1)2.2. Halle Berry is a film star. (Premise 2)Halle Berry is a film star. (Premise 2)3.3. Therefore, Halle Berry is a celebrity. Therefore, Halle Berry is a celebrity.

(Conclusion)(Conclusion)

Bad Argument:Bad Argument:1.1. Some film stars are men.Some film stars are men.2.2. Cameron Diaz is a film star.Cameron Diaz is a film star.3.3. Therefore, Cameron Diaz is a man.Therefore, Cameron Diaz is a man.

Conclusion IndicatorsConclusion Indicators

ThereforeTherefore WhereforeWherefore ThusThus ConsequentlyConsequently We may inferWe may infer AccordinglyAccordingly We may concludeWe may conclude It must be thatIt must be that For this reasonFor this reason SoSo Entails thatEntails that HenceHence It follows thatIt follows that Implies thatImplies that As a resultAs a result

Premise IndicatorsPremise Indicators

SinceSince As indicated byAs indicated by BecauseBecause ForFor In thatIn that May be inferred fromMay be inferred from AsAs Given thatGiven that Seeing thatSeeing that For the reason thatFor the reason that Inasmuch asInasmuch as Owing toOwing to

Example: Expectant mothers should never use recreational Example: Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the drugs, since the use of these drugs can jeopardize the development of the fetus.development of the fetus.

IndicatorsIndicators

Sometimes there are no indicators:Sometimes there are no indicators: (Also, some passages that contain (Also, some passages that contain

arguments contain statements that are arguments contain statements that are neither premises nor conclusions)neither premises nor conclusions)– The space program deserves increased The space program deserves increased

expenditures in the years ahead. Not only expenditures in the years ahead. Not only does the national defense depend upon it, does the national defense depend upon it, but the program will more than pay for itself but the program will more than pay for itself in terms of technological spinoffs. in terms of technological spinoffs. Furthermore, at current funding levels the Furthermore, at current funding levels the program cannot fulfill its anticipated program cannot fulfill its anticipated potential.potential.

Argument Argument ReconstructionReconstruction Break up compound statementsBreak up compound statements Always list premises first, then conclusions:Always list premises first, then conclusions:

P1: The national defense is dependent upon P1: The national defense is dependent upon the space program.the space program.

P2: The space program will more than pay for P2: The space program will more than pay for itself in terms of technological spinoffs.itself in terms of technological spinoffs.

P3: At current funding levels the space P3: At current funding levels the space program cannot fulfill its anticipated program cannot fulfill its anticipated potential.potential.

C: The space program deserves increased C: The space program deserves increased expenditures in the years ahead.expenditures in the years ahead.

Inference & Inference & PropositionProposition

InferenceInference: the reasoning process : the reasoning process expressed by an argumentexpressed by an argument– ““Inference=Argument”Inference=Argument”

PropositionProposition: the meaning or : the meaning or information content of a information content of a statementstatement– ““Proposition=Statement”Proposition=Statement”

HomeworkHomework

Problems: Exercise 1.1Problems: Exercise 1.1– Pages 7-9, Numbers 1-21Pages 7-9, Numbers 1-21

Try these on your own; we will review Try these on your own; we will review some next class some next class

Reading: Chapter 8 (Symbolic Reading: Chapter 8 (Symbolic Logic)Logic)– Pages 299-309Pages 299-309