How to Think: Introduction to Logic, Lecture 4 with David Gordon - Mises Academy
The CategoricalSyllogism (I)How to Think:An Introduction to Logicwith David Gordon
Inference is the process of passingto a new truth.Inference is the third act of the mindThe other two are Conception ---forming an idea of something---andJudgment---connecting twoconcepts, or denying that there is aconnectionDeduction moves from general toparticular. Induction moves fromparticular to general.
Deductive Inference is called a SyllogismIn a Syllogism, there are three propositions:Two Premises and a ConclusionThe premises make the conclusion true. If thePremises are true, the conclusion is true.Be careful about saying the conclusion “must”be true. What is necessary is the wholestatement, “If the premises are true, then theconclusion is true”. Don’t detach theconclusion and say that it is necessary.
All Keynesians are opponents of thefree marketKrugman is a KeynesianTherefore, Krugman is an opponentof the free marketThe conclusion is true but notnecessary---Krugman could changehis mind.
How can you get to a new truth?Through a Middle TermThe Middle Term is found in bothpremises. It is combined with thePredicate of the Conclusion in theMajor Premise. It is combined withthe Subject of the Conclusion in theMinor PremiseIn the Conclusion, the Middle Term(the connection) drops out.
Example: All giraffes are marriedAll men are giraffesAll men are marriedThe Middle Term is giraffes. This is theterm that does not appear in theconclusionThe Major Premise is “All giraffes aremarried” because it contains thePredicate of the conclusionThe Minor Premise is “All men aregiraffes” because it contains theSubject of the Conclusion
Why does the connection enable us toarrive at a new truth?The Subject is included in the class ofthe Middle Term. The Middle Term isincluded in the class of the Predicate.In the example, “giraffes” are in theclass “entities that are married”. “Men”are included in the class of “giraffes”.Thus, “men”, the subject term of theconclusion, is included in the class“entities that are married”, thepredicate of the conclusion.
If one of the premises is negative(an E or O proposition) theexplanation is differentNo hippopotamus is a goalieSome men are hippopotamusesSome men are not goaliesHere the middle term is“hippopotamus”. The Major Premiseexcludes hippopotamuses from theclass of “goalies”The Minor Premise includes “somemen” within the class of“hippopotamuses”
Thus, the conclusion says that“some men”, i.e., the ones who arehippopotamuses, are excluded fromthe class of “goalies”.Note that this syllogism leaves openwhether there are men who are nothippos and, if there are men whoaren’t hippos, whether these menare goalies.
Rules for the Syllogism.The middle term must be distributedin at least one of the premises.With a distributed term, you knowhow much of the class the termapplies to.In our example, “giraffes” isdistributed in the Major Premise, “Allgiraffes are married.” It is notdistributed in the Minor Premise,“Some men are giraffes”. We don’tknow how much of the class of“giraffes” is covered by “somemen”.
If you violate this rule, you committhe fallacy of the undistributedmiddle.All men are marriedSome married people are divorcedAll men are divorced.“Married people”, the middle term,is undistributed in both premises.Thus, the argument isn’t valid.
If a term is distributed in theconclusion, it must be distributed ina premise.All mortals are crazySome men are mortalsAll men are crazyHere, “mortals’ is the middle term. Itis distributed, but this reasoning isstill invalid. “Men” is distributed inthe conclusion, “all men”, but is notdistributed in the premise thatmentions it, “some men”.
A syllogism must have at least onegeneral premise(an A or an E proposition)Otherwise, there would be nomovement from general to particular.Some men are crazySome crazy people are KeynesiansSome men are KeynesiansThis also commits the fallacy ofundistributed middle.
A syllogism cannot have twonegative premises.(E or O propositions)No Misesians are KeynesiansNo Keynesians are MarxistsNo Misesians are Marxists.Even though the conclusion is true,it doesn’t follow from the premises.The premises just exclude Misesiansand Marxists from the class of“Keynesians”. They don’t tell us howMisesians and Marxists are related.
A syllogism cannot contain anequivocal term.All heavy objects are objects thatweigh at least ten poundsHuman Action is a heavy book.Human Action is an object thatweighs more than ten pounds.“Heavy” is used equivocally, tomean both “having a big weight”and “dealing with difficult subjectmatter.”
We will not go into the details, but“Figure” refers to where the middleterm is placed in each premise.For example, in the first figure, themiddle term is the subject of themajor premise and the predicate ofthe minor premise.All mortals are menAll crazy beings are mortalAll crazy beings are men.
“Mood” refers to the type ofpropositions in the syllogism (A, E, I,or O). The example is a valid mood:A, A, A. It is in the first figure.Aristotle thought that it was themost evident form of the syllogism.There are four figures. Syllogismsnot in the first figure can be reduced,i.e., changed to the first figure, butwe won’t go into details.
“Sir Karl Popper has pointed out thatthe idea that one could predict one’sfuture knowledge. . .isphilosophically incoherent: if onecould predict one’s futureknowledge, then one would alreadyknow it.”Tom Palmer, Realizing Freedom,(Cato Institute, 2009), p.444.
“Sir Karl Popper has pointed out that theidea that one could predict one’s futureknowledge. . .is philosophically incoherent:if one could predict one’s futureknowledge, then one would already knowit.”Tom Palmer, Realizing Freedom, (Cato Institute, 2009), p.444.This argument relies on anambiguity in “future knowledge”.This can mean either “knowledgewe don’t have now but will have inthe future” It can also mean“knowledge we have now but willcontinue to have in the future.” Ifyou can predict what you will knowin future, then what you predictwon’t be future knowledge in thefirst sense. It will be futureknowledge in the second sense. All
The states of the Middle East“had all been conjured into existence lessthan one hundred years ago out of the ruinsof the defeated Ottoman empire in WorldWar I…. This being the case, there wasnothing "utopian" about the idea that suchregimes — which had been planted withshallow roots by two Western powers[Britain and France] and whose legitimacywas constantly challenged by internalforces both religious and secular — couldbe uprooted with the help of a third Westernpower and that a better political systemcould be put in their place.”Norman Podhoretz, World War IV,(Doubleday, 2007), pp.144-145.
The states of the Middle East“had all been conjured into existence lessthan one hundred years ago out of theruins of the defeated Ottoman empire inWorld War I…. This being the case, therewas nothing "utopian" about the idea thatsuch regimes — which had been plantedwith shallow roots by two Western powers[Britain and France] and whose legitimacywas constantly challenged by internalforces both religious and secular — couldbe uprooted with the help of a thirdWestern power and that a better politicalsystem could be put in their place.” NormanPodhoretz, World War IV, (Doubleday, 2007), pp.144-145.This is non sequitur. It doesn’t follow fromthe fact that it state doesn’t have deeproots that it is realistic to try to replace itwith something better.
An argument often given againstanarchism is this:Every conflict between protectionagencies requires some otheragency to settle it.Therefore, there must be a centralagency that is the ultimate agencyto settle disputes.
This is a quantifier shift fallacy.It moves from, “Every disputerequires some agency to settleit” to “There is some agencythat must settle all disputes.”This doesn’t follow.Compare, “Everyone has afather” does not imply“Someone is everyone’s father.’