HPS 0611: ArgumentsFall 2015

August 30, 2015

1 Arguments and Science

We often encounter science-related arguments. Scientists themselves makearguments to each other about what the results of their research mean, jour-nalists present arguments to the public about scientific findings, and laypeople make arguments about the credibility of difference scientific evidence.You may have encountered science-related arguments in science journals,press releases, and in conversation.

Here are a few examples of recent science-related arguments.

“Living Near Trees is Good for Your Health”

a team of researchers present a compelling case for why urbanneighborhoods filled with trees are better for your physical health...they found that “having 10 more trees in a city block, on average,improves health perception in ways comparable to an increase inannual personal income of $10,000 and moving to a neighborhoodwith $10,000 higher median income or being 7 years younger.”(Berman notes that self-perception of health is admittedly sub-jective, but adds that it “correlates pretty strongly with the ob-jective health measures” the study considered.)...The results arepowerful because of the size of the study, however, because theyare “correlational,” as scientists put it, they cannot definitivelyidentify the precise mechanism by which trees seem to improvehealth. However, there are some obvious possibilities, including

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one explanation that seems likely to at least partly account forthe results. This is that trees are known to improve urban airquality by pulling ozone, particulates, and other pollutants intotheir leaves and out of the air, and thus, partly protecting peoplefrom them.

But that’s not the only possible explanation. Others, says Berman,include stress reduction that comes from being around greenery –a mental effect that translates into physical benefits – or the possi-bility that being around trees somehow increases ones propensityto exercise. He also suggests that air quality improvement alonemay not be able to explain why people subjectively perceive theirhealth to be better when they live around more trees, in additionto the improvements seen in other health measures – implying apossible psychological factor.1

Ice on Pluto

Observations of Pluto’s surface by the New Horizons spacecraftrevealed a variety of surface features, including mountains thatreach as high as 11,000 feet (3,500 meters), comparable to theRocky Mountains on Earth. While methane and nitrogen icecover much of the surface of Pluto, these materials are not strongenough to support such enormous peaks, so scientists suspect thatthe mountains are formed on a bedrock of water ice.2

Existence of Pentaquarks

Like wishes, bad news, and backup singers, quarks–the elemen-tary bulding blocks of hadronic matter–tend to come in threes...Butquantum chromodynamics, the theory that describes the strong

1Mooney, Chris. 9 July 2015. Scientists have discovered that liv-ing near trees is good for your health. The Washington Post. <http:

//www.washingtonpost.com/news/energy-environment/wp/2015/07/09/

scientists-have-discovered-that-living-near-trees-is-good-for-your-health/

>2Choi, Charles Q. 22 July 2015. Dwarf Planet Pluto: Facts

About the Icy Former Planet. Space.com <http://www.space.com/

43-pluto-the-ninth-planet-that-was-a-htmldwarf.>

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forces that bind quarks together, doesn’t rule out smaller andlarger groupings...CERN’s LHCb collaboration has discovered whatappear to be two pentaquarks. Both are composed of two upquarks, a down quark, a charmed quark, and a charmed anti-quark, but they have opposite parity. The particles, each nearlyfive times as massive as a proton, were identified among the de-cay products of so-called bottom lambda baryons produced inproton-proton collisions. Granted, we’ve heard this story before.In 2003, four independent groups claimed to have observed a lessmassive pentaquark, but the finding was eventually dismissed as astatistical fluke. The new discovery seems to rest on much firmerground. The LHCb collaboration analyzed some 26000 promis-ing decay events–more than 10% of which are thought to haveyielded pentaquarks–and report a statistical significance of morethan 9σ... the particles existence seems nearly certain3

2 Introduction to Arguments

In general, an argument is a set of sentences supporting a claim. Thesupporting sentences are the premises and the supported claim is the con-clusion. There are many types of communication that are not arguments.For instance, expressions of personal preferences (such as “I like dark roastcoffee” or “My cat is cuter than yours”) are not arguments in themselves.Likewise, descriptions (“The beans were roasted for 30 minutes” or“My catis a fat tabby”) are not arguments by themselves. In daily life, argumentsare typically presented by one person (or group) to another, with the aim ofconvincing the latter of the conclusion. Arguments provide reasons and/orevidence for accepting the conclusion. Often, the use of words such as “there-fore”, “as a result”, “consequently”, “for those reasons”, or “hence” indicatethat the author (or speaker) is attempting to make an argument for theclaim that follows them. Premises intended to support the conclusion of anargument are often indicated by such words as “because” and “since”.

Arguments vary in their form and their cogency–how convincing they are.As a result, in order to evaluate the strength of an argument (the strength

3Smart, Ashley G. 27 July 2015. A pentaquark revival. Physicsto-day. <http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.

1063/PT.5.7190;jsessionid=5ig8q5ub3t0k6.x-aip-live-03>

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of the support that the argument provides for the conclusion), it is useful tobe able to identify some different types of arguments. Arguments that aremade in everyday contexts are sometimes incomplete, or the premises are leftimplicit. Moreover, the components of such arguments may not be initiallyeasy to identify due to their integration in ordinary prose. However, withpractice one can learn to extract the important parts of arguments from thecontexts in which they are made and then evaluate those arguments in lightof one’s understanding of good arguments in general.

We will discuss deductive, inductive, and causal arguments below. Wewill also discuss various ways that arguments can go wrong, including logicalfallacies.

3 Deductive Arguments

Deductive arguments are arguments in which the truth of the premisesif true would guarantee the truth of the conclusion. These arguments areparticularly lovely because their form guarantees their validity. That is, nomatter what we substitute for “A”, “B”, “C”, “D”, “M”, “P”, and “S” below(as long as we do so consistently within the argument form), we will get anargument, the truth of the conclusion of which is guaranteed by the truth ofthe premises. Here are some of the most important of such argument forms:

Modus ponens

If A, then BAB

Modus tollens

If A, then BNot BNot A

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Hypothetical syllogism

If A, then BIf B, then CIf A, then C

Disjunctive syllogism

A or BNot AB

Constructive dilemma

A or BIf A, then CIf B, then DC or D

Unconditionally valid categorical syllogistic forms

There are 15 such forms, here are a few of them (optional exercise: generatethe rest):

1.All M are PAll S are MAll S are P

2.All P are MSome S are not MSome S are not P

3.All P are MNo M are SNo S are P

Note that even if an argument is deductive, its conclusion may not infact be true. We can only be sure that if the premises are true then theconclusion will be too. However, determining if the premises are in fact trueis often no easy task!

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We say that deductive arguments are truth-preserving. The truth ofthe conclusion is, in a sense, already contained in the truth of the premises.This point is particularly clear in the case of mathematical proofs, all of whichare deductive arguments. However, despite their loveliness, this means thatdeductive arguments do not really yield new factual information. Psycho-logically, we might be surprised by the conclusion of a deductive argument–especially if there are many steps to the argument (in contrast to the simpleexamples given above). However, if the argument is deductive the conclusiondoes not add anything that was not already present in the premises. Withthis feature in mind, it will be probably be obvious that most argumentsmade in the context of actual scientific practice, or arguments made in thepublic sphere about scientific findings, are not deductive.

Some other useful terminology

Consider a hypothetical proposition of the form “If P then Q”Here, P is the antecedent and Q is the consequent.

Note that the logical connective instantiated here as “If...then...” is thematerial conditional. The material conditional indicates something dis-tinct from causal dependence or generation. For example, speaking aboutcausal dependence we might say “If the branch breaks, then the treehousewill collapse”. However, the material conditional is a logical connective whichneed not involve causal connection at all. For instance, using the materialconditional, we might say “If Alice’s favorite color is blue then Bob’s favoritecolor is red”. There is no causal dependence here.

In this example, we say that Alice’s favorite color being blue is a sufficientcondition for Bob’s favorite color being red. As long as we know that Alice’sfavorite color is blue, we can be sure that Bob’s favorite color is red. Notethat Alice’s favorite color might not be blue and yet Bob’s favorite colorcould still be red. The proposition just states that if it is the case thatAlice’s favorite color is blue, then it will also be the case that Bob’s is red.

Consider instead the proposition “Bob’s favorite color is red only if Chris’favorite color is green”. Here, Chris’ favorite color being green is a necessarycondition of Bob’s favorite color being red. That is, unless Chris’ favoritecolor is green, Bob’s favorite color will not be red. For example, it cannot bethe case that Chris’ favorite color is yellow and Bob’s is red. Bob’s will bered only in cases where Chris’ is green.

Putting these together, the necessary and sufficient conditions for

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something are those, and only those, conditions that are sufficient for it. Wesay “P if and only if Q” or “P iff Q” or “P just in case Q”. The usualexample is: “Being an unmarried man is necessary and sufficient for being abachelor”.

For our purposes, an argument is said to be valid if and only if the truthof its premises guarantee the truth of the conclusion by dint of the form ofthe argument.

An argument is sound if and only if it is valid and its premises are infact true.

An argument that falls short of the very strong threshold of validity yetthat is still a good, convincing argument is said to be cogent. Thus, forexample, one might reasonably accept the conclusion of a cogent inductiveargument in appropriate contexts.

When evaluating the cogency of arguments, we test the argument againstpossible objections. Objections can target the form of the argument inquestion, the truth of one or more of its premises, the relevance of the ar-gument to the question at hand, etc. One common way of objecting to anargument is to procure a counterexample. If my argument for the implau-sibility of extraterrestrial life relies crucially on the nonexistence of otherplanets with liquid water, you could reasonably challenge my argument byproviding evidence for the existence of such planets. Such instances wouldbe counterexamples to the universal statement serving as a premise in myargument, i.e. that there are none.

4 Inductive Arguments

Inductive or ampliative arguments provide some support for their conclu-sions, but do not guarantee them deductively. The conclusion of an inductiveargument in some sense goes beyond its premises–it contains new informa-tion not already present in the premises. In particular, the premises of aninductive argument could all be true, and the conclusion be false. Therefore,in making such arguments, one incurs a certain amount of inductive risk.Here are some important forms of inductive arguments:

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Arguments based on samples

X percent of observed Fs are GsX percent of all Fs are Gs

Arguments from analogy

Objects of type X have properties F, G, H, etc.Objects of type Y have properties F, G, H, etc. and also property ZObjects of type X have property Z

Statistical syllogisms

X percent of all Fs are Gsa is an Fa is a G

5 Causal Arguments

In a causal (NB: not “casual”!) argument, the conclusion is a claim aboutsomething being the cause of something else. For example, a scientist couldmake an argument, the conclusion of which is that cosmic rays caused thefailure the satellite electronics. You can often recognize causal claims viaindicator terms (besides “cause” and “effect”) such as “produced”, “wasresponsible for”, “led to”, “result of”, “induced by” and so on.

The causal arguments that you will typically encounter in your life inthe real world are inductive arguments. How would you go about construct-ing a deductive causal argument? You might try, Sherlock Holmes-style, todetermine all possible causes of some phenomenon and then systematicallyrule them out one by one. This immediately brings us to the sticky philo-sophical topic of possibility. But when have you ever been in a positionto really list all possible causes of anything? How do you know what ispossible? You might think that it is the purview of science itself to tell uswhat is (at least physically) possible or not. Is time travel possible? Thisseems like a scientific question. But if, in the course of doing science, one istrying to determine the cause of something or other, one’s understanding ofthe possibilities will affect one’s ability to conduct a Sherlock Holmes-styleinvestigation. But in this case, there is no “higher” resource to appeal to

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than the scientific body of knowledge in order to construct the list of pos-sible causes in the first place! As a result, even good scientific argumentsfor causal claims usually inherit some epistemic risk deriving from the un-certainty about possible causes. Nevertheless, this strategy can be helpful ineveryday life (think about troubleshooting some device or machine) even ifnot totally foolproof.

Note that in some cases we would like to say that a single, specific Cis the cause of some E. Ingesting hemlock was the cause of Socrates’ death.However, in other cases, we would like to say that multiple causal factorsprecipitated some outcome, e.g. the heavy rain, bad breaks, and the deer’smovements all contributed to the collision.

Mill’s Methods

John Stuart Mill (1806-1873) developed a system of methods to help deter-mine causes. Memorizing the names of the methods isn’t particularly impor-tant. However, explicitly identifying these patterns will help you recognizethem in everyday contexts. The methods are:

Method of Agreement Consider a collection of diverse cases that ex-hibit the same effect. Find some antecedent circumstance present in all suchcases.

Method of Difference Consider a collection of diverse cases, some ofwhich exhibit the same effect and some not. Find some antecedent circum-stance that is present only in the cases for which the effect is observed, andnot the others.

Method of Agreement and Difference Find some antecedent circum-stance that is present when, and only when, the effect is observed.

Method of Concomitant Variation Find some antecedent circum-stance that varies in proportion to the variation of the effect of interest.

Method of Residues By accounting for aspects of a complex effectaccording to one’s prior knowledge of causal relationships, find the remainingantecedent circumstance of the effect of interest.

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Cause and correlation

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4Munroe, Randall. Correlation. Accessed August 30, 2015. <http://xkcd.com/552/>5Church of the Flying Spaghetti Monster. Open Letter To Kansas School Board.

Accessed August 30, 2015. <http://www.venganza.org/about/open-letter/>

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6Correlated: Surprising connections between seemingly unrelated things. Correlation# 1176. Accessed August 30, 2015. <http://www.correlated.org/1176>

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Suppose two attributes are positively correlated. Why might this be? Itcould be that one is the cause of the other (or the other way around)...butit could also be that there is some other common cause of both, or sheercoincidence! Without further case-specific knowledge, we will not be able totell whether there is a causal relationship involved.

Strength of correlation

Consider two attributes (X and Y ) of a group of cases. For example the“cases” could be school districts, the X attribute could be % of college edu-cated residents and the Y attribute could be number of pet owners.

• There is a positive correlation between X and Y if a higher propor-tion of cases with attributeX also have attribute Y than cases that donot have attribute X.

• There is a negative correlation between X and Y if a lower propor-tion of cases with attribute X also have Y, when compared to cases

7Messerli, Franz H. 2012. Chocolate Consumption, Cognitive Function, and NobelLaureates. The New England Journal of Medicine 367: 1562-1564.

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without X.

• There is no correlation between attributes X and Y if cases withattribute X also exhibit attribute Y in the same proportion to caseswithout attribute X.

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6 Fallacies

For our purposes, a fallacy is a faulty argument scheme. There are fallacies,structural errors in reasoning, which are so common that they have acquiredspecific names over the centuries. We want to avoid committing fallaciousreasoning in order to give ourselves the best chance at making (and believing)sound arguments. To guard yourself against mistakes in reasoning, and tomore easily spot these mistakes in the reasoning of others, it is helpful tofamiliarize yourself with some of the most pernicious fallacies.

Affirming the consequent

An argument of the form:

If P then QQP

8esri. ArcGIS Resources: Regression analysis basics. Accessed August30, 2015. <http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/

spatial_statistics_toolbox/regression_analysis_basics.htm>

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Note that the conditional “If P then Q” does not license you to conclude“P” from the basis of “Q”. Note the difference between this fallacy andmodus ponens.

Appeal to authority

Arguing that a claim must be true on the basis of support that claim hasfrom an authority figure. Such reasoning is fallacious when the person iden-tified as the authority is not in fact an expert in a field relevant to the claim,experts in the field disagree about the claim, or if there is reason to thinkthat the called upon authority–despite genuinely being an expert in a rele-vant field–may be subject to a conflict of interest (for example due to fundingsources). For example:

Neil deGrasse Tyson says that climate change is anthropogenicClimate change is anthropogenic

Note that appeals to authority need not always be fallacious. For exam-ple, in appropriate contexts it may be reasonable to appeal to the support ofauthorities with expertise in a field relevant to the claim under consideration.

Begging the question or petito principii

Assuming the conclusion in a premise of the argument purportedly made tosupport that very conclusion. Example:

The Bible is the word of GodGod exists

Arguments that beg the question are said to be circular. Note that themisuse of the phrase “begging the question” when one means something like“raising the question” or “suggesting the question” is a pet peeve for manyphilosophers.

Confirmation bias

The tendency to notice and accept cases that are consistent with our priorbeliefs and to ignore or discount disconfirmatory cases. In other words, abias that selectively filters evidence.

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Confusing cause and correlation

Confusing an association for a causal connection.

Denying the antecedent

An argument of the form:

If P then QNot PNot Q

Consider the conditional “If Terry wants a snack then Buddy wants asnack”. Now, even if Terry doesn’t want a snack (i.e. “not P”), it could stillbe the case that Buddy wants one (especially since Buddy always wants asnack). Note the difference between this fallacy and modus tollens.

Equivocation

An argument that relies on two different senses of the same word. For exam-ple:

Evolution is just a theoryIt should not be taught as fact in public schools

Exercise for the reader: attempt to reconstruct the above argument sketchsuch that it is a complete valid argument by filling in the hidden premises intwo ways, using the word “theory” to mean 1) mere speculation and 2) bestcurrently viable scientific framework.

Fallacy fallacy

Concluding that a claim must be wrong, given that it was the conclusion ofa fallacious argument. A real philosopher’s-philosopher fallacy.

Faulty analogy

An argument by analogy for which the cited similarities are not sufficientlystrong or relevant to support the analogical inference between the primarysubject and the analogue. Consider a famous example, “Thomson’s Violin-ist”:

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I propose, then, that we grant that the fetus is a person from themoment of conception. How does the argument go from here?Something like this, I take it. Every person has a right to life.So the fetus has a right to life. No doubt the mother has a rightto decide what shall happen in and to her body; everyone wouldgrant that. But surely a person’s right to life is stronger and morestringent than the mother’s right to decide what happens in andto her body, and so outweighs it. So the fetus may not be killed;an abortion may not be performed.

You wake up in the morning and find yourself back to back inbed with an unconscious violinist. A famous unconscious violin-ist. He has been found to have a fatal kidney ailment, and theSociety of Music Lovers has canvassed all the available medicalrecords and found that you alone have the right blood type tohelp. They have therefore kidnapped you, and last night the vi-olinist’s circulatory system was plugged into yours, so that yourkidneys can be used to extract poisons from his blood as wellas your own. The director of the hospital now tells you, “Look,we’re sorry the Society of Music Lovers did this to you–we wouldnever have permitted it if we had known. But still, they did it,and the violinist is now plugged into you. To unplug you wouldbe to kill him. But never mind, it’s only for nine months. Bythen he will have recovered from his ailment, and can safely beunplugged from you.” Is it morally incumbent on you to accedeto this situation? No doubt it would be very nice of you if youdid, a great kindness. But do you have to accede to it?

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Hasty inductive generalization

A generalization made on a scant base. For example, a generalization madeon merely anecdotal evidence or from a sample size that is too small or toounrepresentative. For instance:

9Thomson, Judith Jarvis. 1971. A Defense of Abortion. Philosophy and Public Affairs1(1): 47-66.

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This summer was significantly cooler than last summerGlobal warming is so over

Ignorance or ad ignorantiam

Arguments that invoke our ignorance with respect to the truth of some propo-sition in support of a substantive claim about the truth or falsity of thatproposition. It is fallacious to argue as follows:

We do not know the cause of the bleedingThe bleeding is supernatural

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10Almossawi, Ali. An Illustrated Book of Bad Arguments. Accessed August 30, 2015.<https://bookofbadarguments.com/>

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Post hoc or post hoc ergo propter hoc

Reasoning that since A preceded B, A must have been the cause of B. Notethat temporal precedence is a necessary but not sufficient condition for cau-sation. For example:

Sheldon: Oh, hi mom. No, I told you I’d call you when I got home,I’m not home yet. (Walks through door) Alright, I’m home. TheArctic expedition was a remarkable success, I’m all but certainthere’s a Nobel Prize in my future. Actually, I shouldn’t saythat. I’m entirely certain. No, mother, I could not feel yourchurch group praying for my safety. The fact that I’m home safeis not proof that it worked, that logic is Post Hoc Ergo PropterHoc. No, I’m not sassing you in Eskimo talk.

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Red herring

A red herring is an irrelevant claim introduced into an argument that servesto derail the train of reasoning. It’s a digression. For instance:

We can only justifiably hold people responsible for actionsthey perform as free agentsAccording to quantum mechanics, the world is fundamentallyindeterministic

People are not responsible for their actions

Straw man

One attacks a straw man when one argues against a simplified (and oftenclearly untenable) revisionary version of one’s interlocutor’s argument. Forexample, suppose Alice is arguing for the claim that “Teenagers should have

11The Big Bang Theory. The Electric Can Opener Fluctuation. Series 3 Episode 1.Directed by Mark Cendrowski. Written by Chuck Lorre, Bill Prady, Steven Molaro, andMaria Ferrari. CBS, September 21, 2009.Text retrieved from: big bang theory transcripts. Episode 01:–The Electric Can OpenerFluctuation. Accessed August 30, 2015. <https://bigbangtrans.wordpress.com/

series-3-episode-01-the-electric-can-opener-fluctuation/>

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access to sex education resources and free contraception”. Bob would commita straw man fallacy if he responded with “Encouraging ‘free love’ amongstchildren is a terrible idea–it will lead to moral degeneracy, disease, and un-wanted pregnancies”. To avoid committing this type of fallacy, it is wiseto attempt to charitably understand one’s interlocutor’s argument especiallyif you must rephrase what that person has said or make auxiliary premisesexplicit.

Vagueness

Vagueness is not a fallacy per se. However, it contributes to clouded reason-ing so often that it is worth mentioning here. In fact, you will often hearphilosophers ask each other to clarify terms, to be more specific, or be moreprecise. You will often hear them say something like “Well, if by X you meanr, s, t then ...” as they try to refine concepts and terminology employed inan active debate or episode of collaborate reasoning. Similarly, when reason-ers disagree it is often useful to hunt for vague predicates, the looseness ofwhich allows sensible people to diverge in their conclusions. Sometimes (onehopes!) when the relevant clarifications have been made, the reasoners cancome to consensus–or at least better understand the position adopted by theother person.

Some nice fallacy lists

<http://philosophy.hku.hk/think/fallacy/list.php>

<https://owl.english.purdue.edu/owl/resource/659/03/>

<https://yourlogicalfallacyis.com/>

<http://www.txstate.edu/philosophy/resources/fallacy-definitions.

html>

<http://grammar.about.com/od/fh/g/fallacyterm.htm>

<https://bookofbadarguments.com/>

<http://www.iep.utm.edu/fallacy/>

7 General resources

“Think Again: How to Reason and Argue” (Duke University MOOC)<https://www.coursera.org/course/thinkagain>

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August 24, 2015-December 30, 2015Instructors: Dr. Walter Sinnott-Armstrong and Dr. Ram Neta

“Defining Science” (NOVA Podcast Series)<http://www.pbs.org/wgbh/nova/id/defining.html>

Hawthorne, James. Inductive Logic. Stanford Encyclopedia of Philosophy.<http://plato.stanford.edu/entries/logic-inductive/>

8 Worksheet

1. Choose one of the three science-related arguments reproduced in Sec-tion 1 and identify the scientific claim for which the argument offerssupport. Do you find the support offered convincing? Why or whynot?

2. True or false: the conclusion of an argument must be true if the argu-ment is deductively valid. Elaborate.

3. Deductive arguments are rare in science. Why might this be?

4. What are some features of a cogent argument?

5. Consider the following passage:

If time travel was logically possible then the time travellercould return to the past and in a suicidal rage destroy his timemachine before it was completed and murder his younger self.But if this was so a necessary condition for the time trip tohave occurred at all is removed, and we should then concludethat the time trip did not occur. Hence if the time trip didoccur, then it did not occur. Hence it did not occur, and it isnecessary that it did not occur. To reply, as it is standardlydone, that our time traveller cannot change the past in thisway, is a petitio principii. Why is it that the time travelleris constrained in this way? What mysterious force stills hissudden suicidal rage?12

12Smith, Joseph Wayne.1985. Time travel and backward causation. Cogito 3. 58.

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Rewrite the argument given in this passage as a series of premises withthe conclusion “The time traveller cannot change the past”. Why doesSmith suggest that this conclusion is fallacious?

6. Describe at least two problems with using Mill’s Methods as strategiesfor determining the cause of some phenomenon.

7. Is correlation a sufficient condition for causation?

8. True or false: on the basis of the absence of a correlation, we canconclude the absence of a causal relation. [Hint: can you construct avalid modus tollens argument with the first clause as a premise and thesecond as the conclusion? ]

9. Name and describe an additional fallacy (not listed above).

10. Find an instance of someone (a quote from the news, a blog, onlinecomments, popular science magazine, professional journal article, etc.)committing a logical fallacy in the context of an argument supposedlyfor a scientific claim or a claim about science. Provide the offendingquote, name the fallacy, and describe precisely how the fallacy wascommitted in this case. What would be required to rescue the argumentbeing made?

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