Conditionals And Arguments
10/13/10ConceptsConditionals and ArgumentsConditionals A conditional is an if-then sentence:"If . , (then) . In a conditional the clause that follows the"if" is the antecedent; the other clause is theconsequent. Example: If it rains then it pours.antececentconsequent Conditional Antecedent andConsequentDeductive and Inductivearguments: how they differ Validity Necessary and sufficientconditions: how to identify Soundness Logical form Biconditional Contrapositive– Logical and non-logicalexpressions Correspondingconditional– Substitution instance:how to identify Argument Premises andConclusions: how toidentify– Method ofcounterexampleNecessary & Sufficient Conditions The state of affairs described in the antecedent isasserted to be a sufficient condition on the state ofaffairs described in the consequent. The state of affairs described in the consequent isasserted to be a necessary condition on the state ofaffairs described in the antecedentis sufficient forIf it rains then it pours.is necessary forNecessary & Sufficient ConditionsLet’s try some examples! “Necessary” and “sufficient” mean exactly what youthink they mean! “Necessary” means “required”– Being 21 is a necessary condition for drinkinglegally in California. “Sufficient” means “enough”– A blood alcohol level of exactly0.08 is a sufficient condition onbeing legally drunk in California.1
10/13/10Necessary or sufficient?I said expensive wine.1. Being a tiger is a for being an animal.2. Being an animal is a condition for beinga tiger3. Drinking water is a condition forquenching one’s thirst.4. Having a racket is a for playing tennis.5. Pulling the cork is a for drinking anexpensive bottle of wine.Necessary or sufficient?1. Stepping on a cat’s tail is a condition formaking the cat yowl.2. Burning leaves is a condition forproducing smoke.3. Paying attention is a condition forunderstanding a lecture.4. Taking a swim in the North Sea is a forcooling off.5. Opening a door is a for crossing theNot the kind that comes with screw caps.Antecedent is sufficient forconsequent(1) If someone is a mother then they’re female If you know that someone is a mother that isenough to show that the person is femaletherefore being a mother is a sufficientcondition on being female. Being a mother is not a necessary condition onbeing female since you can be female withoutbeing a mother.threshold.Consequent is necessary forantecedent(1) If someone is a mother then they’re female Being female is necessary for being a mother: ifsomeone is not female they can't possibly be amother. Thus (1) says that being a mother is a sufficientcondition on being female and being female is anecessary condition on being a mother.Antecedent sufficientConsequent necessaryIn general, for any conditionalwhatsoever, the antecedent is asufficient condition on theconsequent and the consequentis a necessary condition on theantecedent.2
10/13/10Sometimes it’s not obvious(2) If you study then you passSomething can be both(3) If you didn’t pass then you couldn’t have studied There is a difference between necessary andsufficient conditions Passing is necessary for studying? Huh? Example: in (1), being a mother is sufficient, but Yes! Forget about tense. (2) and (3) are logically equivalent: (3) is thecontrapositive of (2)If P then Q -- contrapositive: If not-Q then not-PBiconditionals (4) For any integers x and y, xy is odd if and only if both xand y are odd (4) says that the oddness of xy is both necessary andsufficient for the oddness of both x and y . Statements of necessary and sufficient conditions like (4)are two way conditionals: each of the conditions isnecessary and sufficient for the other. The standard strategy to prove such biconditionals is toprove that the first condition is sufficient for the secondand then that the second is sufficient for the first.not necessary, for being female while beingfemale is necessary but not sufficient for beinga mother. BUT: some times one thing is both necessaryand sufficient for something else.Both antecedent and consequent arefalse but the conditional is true! (5) If Ralph Nader is elected then I'll eat my hat. (6) Ralph Nader will be elected, therefore I willeat my hat. Someone who asserts (5) is convinced thatneither the antecedent nor the consequent istrue--he is betting against Ralph Nader! (6) is not a conditional but an argument.ARGUMENTSs3
10/13/10ArgumentExample of an argument A group of statements, one or more of which (thepremises) are claimed to provide evidential reasonsto believe one of the others (the conclusion)1.All men are mortal.2.Socrates is a man. Factual claim: premises are asserted, i.e. put forthas true.3.[therefore] Socrates is mortal. Inferential claim: premises provide evidentialreasons to believe the conclusion.1 and 2 are premises;3 is the conclusion.Not everything is an argument “A string of statements asserting or clarifying viewsdoes not an argument make” Not an argument: “I hate Bush. Every time I see his face Iwant to step on it.” (assertion) Not an argument: “I can’t stand Hillary. She’s such a WomanSymptoms of an argument Premise indicators– Since– Because– Conclusion indicatorsof the ‘80s--you can imagine her in a power-suit with shoulder-– Thereforepads out to there and a scarf tied in a bow as a pretend– Sonecktie.” (clarification) Not an argument: “I don’t like Obama or McCain– It follows that– either.”(statement in the interest of being Fair and Balanced)An argument is as anargument does!Example of an argumentPoverty offers numerous benefits to thenonpoor. Antipoverty programs provide jobs An argument makes an inferential claim “The easiest way to identify an argument is tofind the conclusion.” Ask: “What claim is the writer or speaker tryingto get me to accept?”for middle-class professionals in social work,penology, and public health. Such workers’future advancement is tied to the continuedgrowth of bureaucracies dependent on theexistence of poverty. (J. John Palen, SocialProblems)4
10/13/10ConclusionConclusion:what the arguer wants to provePoverty offers numerous benefits to thenonpoor. Antipoverty programs provide jobs The conclusion is typically lessfor middle-class professionals in social work,obvious, more controversial thanpenology, and public health. Such workers’premisesfuture advancement is tied to the continuedgrowth of bureaucracies dependent on the Premises are what we assumeexistence of poverty. (J. John Palen, Socialthe hearer already believesProblems)More arguments Since the good, according to Plato, is thatwhich furthers a person’s real interests, itfollows that in any given case when the good isknown, men will seek it.More arguments PremiseindicatorConclusionindicatorSince the good, according to Plato, is thatwhich furthers a person’s real interestsit follows that in any given case when the goodis known, men will seek it.Look for indicator words. This argumentincludes both a premise indicator and aconclusion indicator. But be careful becausethese are just clues!More arguments To every existing thing God wills some good.Hence, since to love any thing is nothing elsethan to will good to that thing, it is manifest thatGod loves everything that exists.------Thomas AquinasMore arguments ConclusionindicatorTo every existing thing God wills some good.Hence, since to love any thing is nothing elsethanto will good to that thing, it is manifest thatisem orre icat loves everything that exists.PGodind------Thomas AquinasLook for indicator words. This argumentincludes both a premise indicator and aconclusion indicator. But be careful becausethese are just clues!5
10/13/10More arguments To every existing thing God wills some good.Hence, since to love any thing is nothing elsethan to will good to that thing, it is manifest thatGod loves everything that exists.------Thomas Aquinas“Hence” really attaches to “it is manifest ” sothis is the conclusion.More arguments Don’t borrow or lend stuff, because if youlend stuff to a friend, lots of times you don’t getit back and that breaks up the friendship. Andborrowing makes you a careless manager.------Shakespeare made easyThis is the conclusion. On quizzes/tests when Iask you to identify the conclusions ofarguments, paraphrase is ok.More arguments Since private property helps people definethemselves, since it frees people frommundane cares of daily subsistence, and sinceit is finite, no individual should accumulate somuch property that others are prevented fromaccumulating the necessities of life.So the conclusion is typically less obvious andmore controversial than the premises. Theconclusion of this argument is clearlycontroversial!More arguments Neither a borrower nor a lender beFor loan oft loses both itself and friendAnd borrowing dulls the edge of husbandry------William ShakespeareSometimes it helps to paraphrase. Don’t thinkof the conclusion as a piece of text, but as theproposition that the arguer wants to prove—which you can state in your own words.More arguments Since private property helps people definethemselves, since it frees people frommundane cares of daily subsistence, and sinceit is finite, no individual should accumulate somuch property that others are prevented fromaccumulating the necessities of life.Don’t get hung up on premise and conclusionindicators or other textual clues. Rememberwhat an argument is supposed to do, viz. toconvince the hearer of something he doesn’talready believe.Deductive and InductiveArguments Difference in inferential claim Deductive: premises are supposed to force(necessitate, guarantee) the conclusion Inductive: premises are just supposed to makeconclusion probable NOTE: deductiveness and inductiveness are amatter of what is supposed to happen--not allarguments do what they’re supposed to do!6
10/13/10Example: Inductive GeneralizationPremise: 32% of all Nielson households watchThe Simpsons.Conclusion: 32% ( /- 2%) of all AmericanInductive GeneralizationSample: NielsonHouseholdshouseholds watch The Simpsons This is a good inductive argument becauseTarget: AllHouseholdsthe sample is large and fair The premise can’t force the conclusionbecause there’s more information in theconclusion!Other kinds of inductive arguments Analogical induction (“Argument fromanalogy”)– X and Y both have property 1.– X has property 2.– Therefore, Y probably has property 2 also. Abduction (“Argument to the bestexplanation”)–P– E is the best explanation for P– Therefore EArgument from analogy Example– My Nissan Sentra is very reliable--209,000 miles on the clock and it hasn’t given me alick of trouble!– Therefore your Nissan Sentra will probablydo good for you. The Argument from Analogy for Other Minds isprobably the most famous analogy argument inphilosophy.X has property #2X and Y both have Property #1Cogito,ergo sumWe look pretty much the same, behave pretty much thesame and both of us have brains.I think!7
10/13/10Y has property #2Cogito,ergo sumCogito,ergo sumTherefore, (probably) he thinks too!Abduction: inference to the bestexplanationThe best explanation for this is thatthere’s an external world causing myexperiences.Inductive Arguments There’s supposed to be information in theconclusion that’s not in the premises So even in a good inductive argument thepremises don’t necessitate the conclusion I.e. it is logically possible for the premises to betrue and the conclusion false Even though that’s improbableAbduction: inference to the bestexplanationMy experience is coherent, predictable(but sometimes surprising) andsometimes comes to me against my willAbduction: Inference to the Best ExplanationTherefore, there the external world probably exits!Deductive Arguments Premises are supposed to necessitate (“force,”“guarantee”) the conclusion A deductive argument is valid if this reallyhappens: the premises really do necessitatethe conclusion Validity is “internal” to the argument: itconcerns the connection between premisesand conclusion whether they’re true or not.8
10/13/10ValidityA valid argument The premises necessitate (force, guarantee) theconclusion It is not logically possible for the premises to be true andthe conclusion false (“There is no possible world at whichthe premises are true and the conclusion is false”)1.All men are mortal.2.Socrates is a man.3.[therefore] Socrates is mortal. It is truth-preserving: IF the premises are true then theconclusion must be true There is no information in the conclusion that’s not in thepremises (“The conclusion is ‘contained’ in thepremises”) It is not possible to represent the premises withoutrepresenting the conclusionAll men are mortalSocrates is a manmenmenmortalsSocrates is mortalStupid arguments can be valid!1.All Greeks are mathematicians2.Obama is a Greek3.[Therefore] Obama is a mathematiciana 2 b 2 c2menmortals9
10/13/10Same form as Socrates Argument!Soundness Validity all true premises So sound arguments have true conclusions too The Obama argument is valid but not sound!GreeksMathematiciansConditionals can be parts ofargumentsConditionals, Arguments & Inferences Like arguments, conditionals may express inferences. A conditional by itself is not an argument.(7) If you study then you'll pass. If you pass then you'llgraduate. Therefore if you study you'll graduate. Difference: when you put forth an argument you commityourself to the truth of all its parts--even if "only for thesake of the argument.”(8) If a number is even then it's divisible by 2 without a When you assert a conditional, you do not commityourself to the truth of either its antecedent or itsconsequent.remainder. 4 is divisible by 2 without a remainder.Therefore, 4 is even. The whole conditional can be true even if both itsantecedent and consequent are false.Corresponding Conditional For any given argument, the conditional that isformed by taking the conjunction (the "anding") of its premises as the antecedent and theconclusion of the argument as its consequentis the corresponding conditional to thatargument. The corresponding conditional to an argumentis the conditional that expresses the sameinference as the argument.Corresponding ConditionalArgumentConditional1. All men are mortalIf all men are mortal2. Socrates is a manand Socrates is a man3. Therefore, Socrates isthen Socrates is mortalmortalNot anargument!10
10/13/10Validity and Necessary Truth The Socrates argument is validValidity is a matter of form2. Socrates is a man1. All Greeks aremathematicians3. Socrates is mortal2. Obama is a Greek1. All men are mortal Its corresponding conditional is3. Obama is a mathematiciannecessarily true In general, an argument is valid if andonly if its corresponding conditional isnecessarily true.Validity and Truth Value Invalid Valid– True premises/trueconclusion– True premises/true conclusion(sound)– False premises/ vali Ruledb da– False premises/false conclusionofalse conclusion y def rgumut forin– False premises/itio entn strue conclusion– False premises/trueconclusion– True premises/false conclusionSame logical formBoth argumentsare substitutioninstances of thisform1. All S are P2. X is an S3. X is a PLogical form Logical expressions: all, no, some, are, not,and, or, if-then, if and only if . . . Non-logical expressions: “content” words, e.g.men, mortal, mathematician, Greek, Socrates,Obama . . . We can’t give a firm list of logical expressionsapart from a system of formal logic that studiesthe their behavior so for now we’ll leave itintuitive.Same logical form Same logical expressions Same pattern of same non-logical expressionsSo, what’s thelogical formof this?All dogs are mammalsAll ants are insectsAll mammals are vertebratesAll insects are arthropodsAll dogs are vertebratesAll ants are arthropods11
10/13/10Different logical formValidity is a matter of form If two arguments are of the same form thenAll dogs are mammalsAll cats are vertebratesAll mammals are vertebratesAll mammals are vertebratesAll dogs are vertebratesAll cats are mammalsthey’re either both valid or both invalid Is this true? No. But we will define “validity” as “formalvalidity” to make it true.Why not formally valid?Valid but not formally validGeorge is a bachelorGeorge is a bachelorDucati is a dogGeorge is not marriedDucati is not warm-bloodedTherefore, George is not marriedThe argument at left is valid but its validity doesn’tcome from its form. We resolve to ignore sucharguments!We stipulate that from now on “valid” means“formally valid”!Given our definition of validity Arguments of the same form are the same asregards validity/invalidity– So, if one argument of a given form isinvalid, so are all other arguments of thesame form If an argument has all true premises and afalse conclusion then it must be invalidThe Method of Counterexample To test an argument for validity, we try to find anotherargument of the same form that has all true premisesand a false conclusion. If we can find such an argument then, given ourdefinition of validity, the original argument is shown to beinvalid If we can’t, it shows nothing!12
10/13/10CounterexampleArgument C is a counterexample to Argument A iff1. A and C are substitution instances of thesame logical form, and2. C has all true premises and a falseconclusionExample1. All dogs are vertebrates1. All x 2 are x 12. All mammals are vertebrates2. All x 10 are x 13. All dogs are mammals3. All x 2 are x 10These arguments are of the same form so must be thesame as regards validity/invalidity. The argument at theright must be invalid because it has all true premisesIf an argument has a counterexample then itand a false conclusion so the argument at the left mustis invalid!be invalid also. The argument at the right is a“counterexample” to the argument at the left.So, what do I have to know aboutthis stuff for the quiz? Arguments and conditionals (see handout) How to recognize the conclusions of arguments(multiple choice) Determining when 2 arguments are of thesame form, when one is a counterexample toanother, and what that shows about (in)validity.13
Example of an argument 1. All men are mortal. 2. Socrates is a man. 3. [therefore] Socrates is mortal. 1 and 2 are premises; 3 is the conclusion. Not everything is an argument “A string of statements asserting or clarifying views does not an argument make” Not an argument: “I hate Bush. Every time I see his face I
MATLAB Programming Tips 16 Function Arguments This section covers the following topics: “Getting the Input and Output Arguments” “Variable Numbers of Arguments” “String or Numeric Arguments” “Passing Arguments in a Structure” “Passing Arguments in a Cell Array” Getting the Input and Output Arguments Use na
Lecture Notes: Probability of Conditionals in Modal Semantics Justin Khoo and Paolo Santorio November 4, 2018 . Foundations of modal and conditional semantics and Stalnaker’s Thesis Formal Preliminaries Let Wbe a set of worlds, and Fbe a set of subsets of Wthat is closed under . (9
4: Conditionals 75 1. Circle the eight examples of if and the two examples of wish in the passage. 2. Write the line numbers of the four if clauses that have simple past tense verbs. Write the subject-verb combinations from both the if clause and the main clause. The first one has been done for you as an example.
def max(x,y): """Returns: max of x, y""" # simple implementation 1 if x y: 2 return x 3 return y max(0,3): 9/16/21 Conditionals & Program Flow 18
Lecture 8: Conditionals & Control Flow (Sections 5.1-5.7) CS 1110 Introduction to Computing Using Python [E. Andersen, A. Bracy, D. Fan, D. Gries, L. Lee,
Command Line Arguments It is standard and safe programming practice for main to immediately check to see if it has received the correct number of arguments from the Linux command line. If there is a mismatch, main prints out a proper usage statement and immediately ends the program. Systems Programming Command Line Arguments 5
One particularly useful case is handling coroutine resume arguments, since no support is provided by the core for handling these beyond just supplying the list of arguments it was called with. A bit of boilerplate allows parse args to be neatly slotted into place to handle these arguments: coroutinefoo apply[list{}{setres{} setoptions{-code0 .
VLAAMS SUPERCOMPUTER CENTRUM Command line arguments Interpreted by the command itself usage depends on the command Order of arguments often doesn't matter. Convention: options frst, non-option arguments last. Short options can be combined, i.e. date -R -u date -Ru For some commands, strict rules apply, e.g. find Meaningof arguments Non-option argument: often a fle name
