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1- IntroductoryLecture.pdf

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Buffalo State College
James Hildebrand

This is a course in basic formal logicIn this first lecture I do three thingstell you what basic formal logic is about and why it is worth studyingdescribe what is involved in studying itgive you an introduction to some fundamental logical concepts that we will be using throughout this courseoutline the courseThe fundamental logical concepts I will be introducing you to aresentenceargumentsame sentencecontradictory sentencederivabilityA number of remaining fundamental concepts fall into one or other of two groupsConcepts based on derivability Concepts based on contradiction deductive validity and logical entailmenttheorem and antitheorem logical truth falsity and indeterminacyinterderivability logical equivalencecontradiction logical inconsistency1THE SUBJECTFORMAL LOGIC is the study of one component of good reasoningWhen we reason we start off with a collection of claims that we take to be true called premises and we draw conclusions from those premisesThese conclusions can be added to our premises and used to draw yet further conclusionsIf our premises are true and we use good reasoning we will arrive at true or at least probably true conclusionsIf our reasoning is bad we will only arrive at true or probably true conclusions by accidentHere is an example of good reasoningIn giving the example I display the reasoning in standard form listing the premises first followed by a horizontal line followed by the conclusionI have five toes on my left foot The left and right sides of animals are generally approximate reflections of one another I have five toes on my right footHere is an example of bad reasoningI have five toes on my leftfoot Stephen Harper is PrimeMinister of CanadaIn the first case the reasoning is good even though the conclusion might for any of a number of causes be falseIn the second the reasoning is bad even though the conclusion is true at the momentOne thing that makes reasoning good or bad is its formDifferent arguments can all follow a common form or patternHere are some examplesAll As are Bs Some As are Bs a b and c are As All Bs are Cs Some Bs are Cs d is like a b and c All As are CsSome As are Csd is an A If P then Q If P then Q a is a B But notP P Most Bs are Cs NotQQa is a C We can plug different things in for the letters in these patterns for A B and C names of groups of things for a b c and d names of individual things and for P and Q entire sentences and so generate different argumentsTake the first of the above examplesPlugging in group names for A B and C givesAll lawyers are greedy All greedy people are untrustworthy All lawyers are untrustworthy Here A is lawyers B is greedy people C is untrustworthy peopleNote that when you plug in these names you must put the same thing for each letter wherever it occursSo having started off taking A to be lawyers you must keep putting lawyers for A wherever else A occurs in that patternPlugging in different group names gives us different argumentsAll whales are sea creatures All sea creatures are fish All whales are fish All cats are felines All felines are mammals All cats are mammals And so onNote that as different as all of these three arguments are all of them have the same formIt is the business of formal logic to identify the different forms of arguments and of the sentences that compose them and to specify what those forms contribute to making reasoning good or badFormal logic is also called SYMBOLIC LOGICFormal logic ends up being symbolic because when you want to describe the form of an argument as I did above it is not possible to write in sentences or namesThat would make it uncertain what parts of the argument you wrote down are the parts that have to do with the form and what parts are the parts that arise from plugging particular sentences or names into that formTo make the form appear we need to use symbols to stand for the names or sentences that get plugged into the formDEDUCTIVE AND INDUCTIVE FORMAL LOGICLogicians have discovered that some argument forms are good whereas others are badThe good forms are good in one or other of two senses that they do not permit you to combine true premises with a false conclusion or that they employ premises that establish some likelihood of the truth of the conclusionSo regardless of what you take the letters to stand for as long as they stand for things that give you true premises you will end up with a conclusion that is true or at least likely to be trueLogicians refer to the forms that will not allow combining a false conclusion with true premises as deductively good formsThey refer to the forms that employ premises that establish a likelihood of the truth of the conclusion as inductively good formsThe first of the forms I listed earlier is a deductively good formRegardless of what group names you plug in for A B and C you cannot end up with an argument that has all true premises and a false conclusionThe conclusion will be false only if at least one of the premises is also falseDeductively bad argument forms are deductively bad because there is at least one way of taking the letters to stand for things that give you true premises but a conclusion that is falseThe second of the forms I listed earlier is like thisWhile there are many ways of plugging in group names for A B and C that will give you true premises and a true conclusion there is at least one that will notSome cats weigh over 12 pounds Some animals weighing over 12 pounds are dogs Some cats are dogs The premises of this argument are both true but the conclusion is falseThat makes the argument form Some As are Bs and some Bs are Cs so some As are Cs a deductively bad formIt does not matter that other substitution instances give you true premises and a true
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