An Informal Fallacy Primer

Although it is not infallible, logic can be useful in a number of different contexts. Some people tend to take logic to the extreme, and maintain that it is the only path to knowledge. I find this position rather suspect, as even the most rigorous application of logic can lead to contradictions (perhaps the simplest example being the liar paradox, i.e., "This statement is false") and prefer to regard logic as a way to evaluate the internal consistency of various truth claims, and therefore a useful tool for critical thinking. As critical thinking is a vital component of democracy, one would expect that a society that values democracy would promote critical thinking. In my experience, however, critical thinking is rarely a part of formal education (at least in the United States), basic logic included. Even at the university level, critical thinking skills are rarely prioritized, even in post-graduate studies. I probably would never have learned basic logic were it not for the efforts of an excellent professor, Dr. Jay Harman (now deceased), who took the time to introduce me and several other students to critical reasoning in an undergraduate course on environmental ethics. While I cannot claim anything near perfection, I believe that I have grasped enough of a basic understanding of the principles of logic to identify internal flaws in many arguments I hear. Although logic itself is much more than a list of fallacies, I have decided to focus on the informal fallacies in this article because they address many key concepts and because they might whet your appetite for a deeper understanding. Writing this primer is helping me to refresh my knowledge of this subject matter, and the result will hopefully help you identify some of the basic fallacies of informal logic.

The sequence, grouping and definitions of the items listed here are based on Copi and Cohen's worthy text, Introduction to Logic, with variations of my own and from alternate sources. Introduction to Logic is a very well-written and accessible textbook, and I highly recommend it to anyone even mildly interested in the topic. To help illustrate the structures of and differences between the fallacies, I have included examples of most of the fallacies listed. When I could find them, I included illustrative examples from other websites or media sources. Many examples, however, are simply fictional accounts generated solely for illustrative purposes. As I encounter better examples, I will replace these fictitious examples with actual instances. I would also welcome any examples you would like to send along. Just mention them in a comment below or use my contact page to send them along.

Note to readers: I have recently reviewed this article and find that a number of topics are outdated or could be significantly improved by revision. As time permits, I will undertake such revisions. --BMN, 21/09/2015

Article Contents

  1. Informal vs. Formal Logic
  2. Propositions and Arguments
  3. Four Classes of Informal Fallacies
    1. Fallacies of Relevance
      1. R1) Argumentum ad Populum -- Appeal to Emotion
      2. R2) Argumentum ad Misericordiam -- Appeal to Pity
      3. R3) Argumentum ad Baculum -- Appeal to Force
      4. R4) Argumentum ad Hominem -- Against the Person
      5. R5) Ignoratio Elenchi -- Irrelevant Conclusion
    2. Fallacies of Defective Induction
      1. D1) Argumentum ad Ignorantiam -- Argument from Ignorance
      2. D2) Argumentum ad Verecundiam -- Argument by Authority
      3. D3) Non Causa Pro Causa -- Questionable Cause
      4. D4) Converse Accident -- Hasty Generalization
    3. Fallacies of Presumption
      1. P1) Accident
      2. P2) Plurium Interrogatum -- Complex Question
      3. P3) Petitio Principii -- Begging the Question
      4. P4) False Dilemma (False Dichotomy)
    4. Fallacies of Ambiguity (Sophisms)
      1. A1) Equivocation
      2. A2) Amphiboly
      3. A3) Accent
      4. A4) Composition
      5. A5) Division
  4. Conclusion
  5. See Also
  6. Recommended Texts
  7. Footnotes

1. Informal vs. Formal Logic

I am particularly fond of Stoll's definition of logic as "an analytical theory of the art of reasoning whose goal is to systematize and codify principles of valid reasoning". Copi and Cohen offer a slightly simpler definition of logic as "the study of the methods and principles used to distinguish correct from incorrect reasoning". Reasoning, in turn, may be defined as the methods we use to arrive at or justify a belief. Finally, a belief may be defined as something we hold to be true about reality. All three of these definitions are largely over-simplified, but they will suffice for the current purposes. Any deeper examination of the ontology of logic is outside the purview of this article.

The realm of logic that deals with the content of arguments is referred to as informal logic. The role of informal logic is to standardize the methods used to move from the propositions to the conclusion(s). Formal logic, on the other hand, does not concern itself with the meaning or content of an argument, and assesses its correctness solely by form of the propositions. The field of mathematics is an excellent example of a system of formal logic. I highly recommend you consult Copi and Cohen's text if you're interested in informal logic, and Stoll's text if you're interested in formal logic.

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2. Propositions and Arguments

Put briefly, an argument is a collection of propositions in which at least one of the claims is said to follow from the others. A proposition is an assertion that something is or is not so, and is always true or false. Propositions used to support a given argument are commonly labeled premises, while those that the premises support are commonly labeled conclusions. The question of which propositions are the premises and which are the conclusions depends largely on the given argument and may not always be clear. While propositions are considered either true or false, arguments are either valid or invalid. The validity of a given argument is based solely on whether or not the premises support the conclusion, and not on whether the conclusion (or any of the premises) are true or false. This implies that one could very easily have an argument that consists entirely of false propositions but is still valid.

p1) Bob Dole is an evil cyborg.

p2) Evil cyborgs shoot lasers from their eyes.

erego,

c1) Bob Dole shoots lasers from his eyes.

Example 1. An argument with false premises (presumably) and a false conclusion (again, presumably).

The important point to note here is that the validity of the argument is evaluated independently of the truth of its prepositions. As a result, one can have an equally valid argument with all false propositions, all false premises and a true conclusion, or mixed premises and a true or a false conclusion. One situation you cannot have, however, is a valid argument with all true premises and a false conclusion. This is impossible because a valid argument's premises support its conclusions, and therefore all true premises must inevitably yield a true conclusion. Another way of stating the question of validity is, 'Assuming that they are all true, do(es) the conclusion(s) follow logically and necessarily from the premises?'. If the answer is yes, then the argument is valid. The table below might help to illustrate the possibilities:

Conclusion
True False
Premises True Valid Invalid
False Valid Valid

Table 1. The matrix of possible relationships between the validity of an argument and the accuracy of its propositions.

The reason I'm going to such lengths to clarify the difference between truth and validity is that informal logic is concerned solely with the question of validity. One implication of this limitation is that an argument containing a fallacy may still be true, even if it is invalid. The ability to identify informal fallacies will not necessarily help you 'win' an argument; it will merely help to ensure that both parties 'fight fair'.

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3. Four Classes of Informal Fallacies

Now that the basics have been covered, we can move on to the main part of this article. I have decided to follow Copi and Cohen's example and group fallacies into four general classes based on the nature of the gap between the premises and the conclusion. Briefly, these four classes are the fallacies of relevance, the fallacies of defective induction, the fallacies of presumption and the fallacies of ambiguity. I will first identify fallacies by their Latin names if I know them, and then provide the English translations.

R) Fallacies of Relevance

Fallacies in this class are characterized by the absence of a valid connection between the premises and the conclusions drawn. Instead, they tend to rely on other devices to draw attention from the fact that their conclusions are unsubstantiated. Election campaigns and advertisements in general are great places to find these sorts of fallacies.

R1) Argumentum ad Populum -- Appeal to Emotion

The literal translation of argumentum ad populum is "appeal to the populace", which is where this fallacy is most frequently used. While an argument over an important issue may indeed stir up emotions, one must never let an emotional reaction subvert the role of reason in an argument. An argumentum ad populum is designed to do just that; its user attempts to manipulate the emotions of the audience rather than to present evidence or rational arguments. Often, the blatant attempts to manipulate emotions are easy to spot in an instance of ad populum. Sometimes, however, the manipulation can be quite subtle. Social scientists, for instance, have found that the emotional connotation of the phrasing in surveys will significantly influence the results. Advertising is an excellent place to look for examples of this fallacy. The goal of modern advertising is to create a perceived need for a given product, and emotional manipulation is a very effective way to do so. Political campaigns and speeches are also replete with instances of ad populum (among other things). Take, for instance, Anne Coulter's approach to the debate over the question of whether government interrogators ought to be allowed to defile the Qur'an in their interrogations:

Liberals believe in burning the American flag, urinating on crucifixes, and passing out birth control pills to 11-year-olds without telling their parents -- but God forbid an infidel touch a Quran at Guantanamo.

Example 2. An example of argumentum ad populum in the torture debate. From Ann Coulter, 24 October 2007, Have You Hugged an Islamo-Fascist Today?, anncoulter.com.

Note that, in addition to purposefully using emotionally inflammatory images, this argument fails to distinguish between the right of individual expression and government endorsed defilement of a text sacred to a given religion (i.e. the debate is not over whether individuals should be allowed to defile the Qur'an, but whether the government ought to be doing it as part of an ethically questionable interrogation program). Rather than address the true issue, the argument uses fear and outrage to make its case. While blatant instances of argumentum ad populum can be rather humorous, the more subtle instances can be very dangerous to honest debates. On the other hand, most people hate to think that they can be manipulated, so perhaps the most effective counter to this technique when it's used against someone is to call the offender out on it. An ideal counter would encourage both the offender and the audience to look past the emotional rhetoric and to handle the issue with reason and honesty. One must be careful not to use the character indictment brought on by her opponent's willingness to resort to ad populum argument in support of her own case, however, lest she be guilty of argumentum ad hominem.

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R2) Argumentum ad Misericordiam -- Appeal to Pity

The argumentum ad misericordiam, or the appeal to the pitying heart, attempts to exploit the character of mercy in its victim. I personally consider it a specific form of argumentum ad populum. This fallacy is most commonly used to justify a course of action, and therefore appears frequently in legal proceedings. Stories of a skilled attorney winning a favorable ruling in the absence of evidence by merely appealing to the jurors' sense of pity are popular in films and novels. While mercy is an important part of one's character, it must operate within the bounds of reason. The argumentum ad misericordiam attempts to exploit that mercy to justify something that would be otherwise inappropriate. A rather dramatic example of this tactic is employed very skilfully by Osama bin Laden in his account of the 1982 attack by U.S. and Israeli forces on Lebanon:

I couldn't forget those moving scenes, blood and severed limbs, women and children sprawled everywhere. Houses destroyed along with their occupants and high rises demolished over their residents, rockets raining down on our home without mercy.

The situation was like a crocodile meeting a helpless child, powerless except for his screams. Does the crocodile understand a conversation that doesn't include a weapon? And the whole world saw and heard but it didn't respond.

In those difficult moments many hard-to-describe ideas bubbled in my soul, but in the end they produced an intense feeling of rejection of tyranny, and gave birth to a strong resolve to punish the oppressors.

And as I looked at those demolished towers in Lebanon, it entered my mind that we should punish the oppressor in kind and that we should destroy towers in America in order that they taste some of what we tasted and so that they be deterred from killing our women and children.

Example 3. The use of argumentum ad misericordiam in one of bin Laden's videos. From Al Jazeera. Tuesday, 2 November 2004.

The United States has been mistreating people in the Middle East for a long time, and Osama bin Laden's anger with the United States may very well be justified. According to the principles of international law, this outrage does not, however, justify a violent retaliation against explicitly civilian targets. Deliberately targeting innocent civilians in attacks like those executed on 11 September is not an acceptable response, and sympathy for victims of previous U.S. and Israeli attacks should not be construed as an excuse to perpetuate violence against noncombatants. Thus, while one may sympathize with the plight of the people Osama bin Laden claims to be defending, his response is no more appropriate than the injustices he is decrying. The last paragraph in example 3 is also an instance of tu quoque, which we will discuss in R5.

An appeal to pity is very difficult to guard against, as the ability to exercise mercy is arguably one of humanity's most endearing traits. On the other hand, pity should not be substituted for reason. The best defense against this tactic is probably the same as with ad populum, which is to call the opponent out on it and request that his arguments be presented for objective review without the emotional overtures.

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R3) Argumentum ad Baculum -- Appeal to Force

The argumentum ad baculum (lit. appeal to the staff) is a favorite of tyrants everywhere. This obviously fallacious argument uses force, or the threat thereof, to support its conclusions. The threat to which this argument appeals may be physical violence, but it may also be something less tangible. Threats to one's livelihood, property, reputation or family may also be made in an argumentum ad baculum. In the United States, the threat of litigation is often used in the absence of a reasonable argument to force a party or organization to agree to a controversial action or rescind a critical comment. Particularly in cases where the cost of legal representation and litigation would be more than the concessions being demanded, this threat of litigation is enough to allow the side with "deeper pockets" (i.e. more funds available) to win. In addition to litigation, the argumentum ad baculum can be used very subtly in professional environments. In the particularly disturbing example from the New York Times below, senior officials in the White House and the Pentagon are alleged to have threatened military analysts for several major television and news networks into publicly supporting the Bush Administration's war efforts. According to the report, analysts who criticized the Administration's efforts would no longer have access to the information being provided to the group.

On Aug. 3, 2005, 14 marines died in Iraq. That day, Mr. Cowan, who said he had grown increasingly uncomfortable with the "twisted version of reality” being pushed on analysts in briefings, called the Pentagon to give “a heads-up" that some of his comments on Fox "may not all be friendly," Pentagon records show. Mr. Rumsfeld’s senior aides quickly arranged a private briefing for him, yet when he told Bill O’Reilly that the United States was “not on a good glide path right now” in Iraq, the repercussions were swift.

Mr. Cowan said he was "precipitously fired from the analysts group" for this appearance. The Pentagon, he wrote in an e-mail message, "simply didn’t like the fact that I wasn’t carrying their water."

Example 4. An example of a subtle use of argumentum ad baculum. According to the story, military analysts for major media networks were threatened with the loss of access to special briefings if they criticized the Bush Administration's war efforts. From David Barstow, 20 April 2008, "Behind TV Analysts, Pentagon's Hidden Hand", The New York Times.

Any time a threat, no matter how subtle, is introduced in place of a reasonable argument, the threatening party is guilty of argumentum ad baculum. Unfortunately, this is a rather difficult fallacy to counter if the other party is in the position to make good on her threat, and no third party is available for appeals. In the United States, so-called "whistle blower" laws exist to protect individuals from ad baculum in the workplace (the government then acts as the third party), and various international laws have been established to prevent a stronger nation from forcing its will on weaker one (albeit these laws are often ignored). Probably the best thing that can be said about ad baculum is that it is effective only so long as the threatening party is in a position to make good on its threat. The instant the power to enforce the threat dissipates, the threatened party can and usually will retaliate against the threat of force. Unfortunately, in the case of tyrannical governments, this threat of force can persist for generations. Ultimately, reason, and not force, must guide the debate if logic is to prevail.

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R4) Argumentum ad Hominem -- Argument Against the Person

All too often, an opponent will resort to attacking a person's character or reputation if he cannot find a suitable counter to a position held by that person. Copi and Cohen classify ad hominem attacks as either abusive or circumstantial, based on the nature of the attack. Personal attacks on an individual's intelligence, morality, integrity, or character all fall into the abusive category, while insinuations that a person's employment, race, gender or some other vested interest has influenced her conclusions fall into the circumstantial category. While the abusive form of ad hominem is usually more damaging to the opponent receiving the attack, it also tends to be more obvious, and therefore easier to confront. While distracting, the damage inflicted to the opponent's character can still be separated from his stance in an argument, thereby allowing the debate to continue. The circumstantial form, on the other hand, can effectively eliminate any possibility of continuing a reasonable discourse by contending that the opponent's arguments are guided by something other than the pursuit of the truth. Consider the following two (fictitious) examples, where two researchers debate the outcome of an experiment:

Researcher 1: My experiment indicates that an individual internal combustion engine releases x parts-per-million of carbon dioxide. Comparing this to the number of vehicles presently operated in the United States, I estimate that U.S. vehicle use is responsible for approximately y percent of global CO2 emissions. Therefore, reducing the number of vehicles operated in the U.S. should significantly reduce CO2 emissions. Finding an alternative energy sources would drastically reduce emissions.

Researcher 2: Don't you and your spouse both drive SUVs? You really are some kind of hypocrite! Your results are meaningless!

Example 5. An example of an abusive ad hominem argument. The actual argument presented, that reducing vehicle use would reduce emissions, is unaffected by whether or not Researcher 1 is an hypocrite (something we cannot accurately judge without further information).

Researcher 1: My experiment indicates that an individual internal combustion engine releases x parts-per-million of carbon dioxide. Comparing this to the number of vehicles presently operated in the United States, I estimate that U.S. vehicle use is responsible for approximately y percent of global CO2 emissions. Therefore, reducing the number of vehicles operated in the U.S. should significantly reduce CO2 emissions. Finding an alternative energy sources would drastically reduce emissions.

Researcher 2: You're a member of the Union of Concerned Scientists. All you guys do is push your agenda on people. I don't buy your conclusions.

Example 6. An example of a circumstantial ad hominem argument. Researcher 2 is effectively (and in this case not very subtly) accusing Researcher 1 of forging her results to advance a political agenda.

This example also points out another important feature of argumentum ad hominem. While the agenda of Researcher 1 may merit some consideration, Researcher 2 is obligated to examine his colleague's methods and results before making any sort of conclusions. Moreover, accusing another researcher of falsifying her results is a very serious charge, and doing so in the absence of any evidence is outright slanderous. Occasions may arise, such as in courtroom testimonies, where the circumstances favor an individual supporting a particular conclusion. In cases where a biased account is not improbable, the use of ad hominem is not considered entirely fallacious. An ad hominem attack becomes a fallacy when it is used (consciously or otherwise) as a means to divert the argument away from the evidence supporting it. When compared to the seriousness of the accusations made in a circumstantial attack, the abusive form of argumentum ad hominem can appear almost innocuous or humorous. Too often, however, the abusive form can be just as damaging to its victim and a reasoned debate as the circumstantial form.

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R5) Ignoratio elenchi -- Irrelevant Conclusion

The last fallacy of relevance covered here is the Irrelevant Conclusion, or Ignoratio elenchi (ignorance of refutation). An ignoratio elenchi can actually be a valid argument--the fallacy lies in the fact that it is irrelevant to the issue being debated. This category includes fallacies such as the 'Red herring', a deliberate attempt to divert a debate away from the original issue, and 'Tu quoque', an assertion that, because one party violates the principle set forth, the principle is no longer valid. A pair of users on Digg was kind enough to provide an example of tu quoque in his response to a comment on the issue of torture and abuse of prisoners in Iraq and Afghanistan:

Comment
The lack of outrage on the part of the American people on this issue has been astounding. Before this happened, I never would have believed that the American people would openly endorse the abduction, torture and murder of other human beings. Hopefully the Supreme Court's recent decision will help the United States to remember its commitment to freedom and justice.

Response
They weren't tortured or murdered you imbecile. Compare what the murderous muslims do to their pows. They cold blooded murderers should have been executed.

Example 7. An example of a tu quoque form of an ignoratio elenchi. Torturing prisoners is, according to the Geneva Conventions and the Convention against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment unacceptable, regardless of whether or not the prisoners in question would torture their own prisoners. Note how this attack is coupled with an ad hominem attack, and never actually offers any justification for the initial proposition (that no torture took place). The full discussion is available at http://digg.com/politics/Fiasco_0569_Fmr_Iraqi_Detainees_Sue_Military_Contractors.

Tu quoque is usually most effective at diverting the argument when used in conjunction with the ad hominem. The above example does this by referring to the prisoners in question as "murderous Muslims" and "cold blooded murderers". The 'Straw Man' fallacy is also an effective way to divert an argument. In this case, a party refutes a position that appears to be, but is not truly, his opponent's position. Often, the position being refuted in this fallacy is weaker than the actual position, and therefore easier to negate. The name of 'Straw Man' is quite apropos to this fallacy, as the connotation is of combat with a dummy in place of a true opponent.

Because they are cases of the arguments not supporting the conclusions, all of the previously described fallacies may technically be considered specialized forms of ignoratio elenchi. Common usage, however, narrows the definition of ignoratio elenchi to arguments that prove a conclusion that is irrelevant to the issue at hand. Often, ignoratio elenchi also acts as a 'miscellaneous' category that encompasses fallacies of relevance other than those listed here.

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D) Fallacies of Defective Induction

Fallacies of Relevance are so-called because the premises are largely irrelevant to the conclusion. In Fallacies of Defective Induction, the premises are not necessarily irrelevant, but they provide insufficient justification for the conclusions to which they are attached. These sorts of arguments leave a significant conceptual gap between the premises and the conclusion. Both the Fallacies of Relevance and those of Defective Induction fall into the larger pool of non sequitur (Latin, 'it does not follow') because the premises do not lead to the conclusions.

D1) Argumentum ad Ignorantiam -- Argument from Ignorance

An argumentum ad ignorantiam can go two different directions: the conclusion may be declared true just because it has not been proven false, or it may be declared false just because it has not been proven true. In some cases, the threshold for determining when a speaker is guilty of argumentum ad ignorantiam is rather subjective. Arguments with premises whose veracity cannot be reasonably tested may also fall into this category of fallacies, as do arguments that rely on the immutability of the status quo (i.e. the current state of things). Conversely, failing to draw a conclusion in instances where evidence in favor of a given outcome has been actively sought but not found is also an example of ad ignorantiam. This reverse form only applies when the methods used to seek the evidence could reasonably be expected to yield it, and the threshold of evidence required is not always clear. Many scientists accused President Bush of this fallacy when he contended that more research was needed to establish the role of CO2 emissions in global climate change. The following example, quoted from an article attacking Theistic Evolution, demonstrates the use of argumentum ad ignorantiam to 'prove' a premise.

The doctrines of creation and evolution are so strongly divergent that reconciliation is totally impossible. The theistic evolutionists attempt to integrate the two doctrines; however such syncretism reduces the message of the Bible to insignificance. The conclusion is inevitable: There is no support for theistic evolution in the Bible.

Example 8. An example of argumentum ad ignorantiam regarding Biblical support for Theistic Evolution (which essentially proposes that a diety may be the one directing the course of evolution supernaturally). Given the cultures into which the Judeo-Christian scriptures were introduced, one should not be at all surprised to learn that evolution isn't really covered in them. These same scriptures also don't offer any support for the existence of Deoxyribonucleic Acid (DNA), yet most reasonable people are certain of its existence. While reasons to reject theistic evolution might exist, the absence of support for it in the Bible is not one of them. From Werner Gitt, Creation Magazine, Sep-Nov 1995, Vol. 17, No. 4, pp. 49-51 http://christiananswers.net/q-aig/aig-c015.html.

A rare but important exception to the rule that an appeal to ignorance is a fallacy lies in the standard of jurisprudence in the U.K. and the U.S. Historically, an appeal to ignorance regarding certainty of a defendants guilt in a court of the United Kingdom or the United States would not be considered fallacious. This is because both nations' legal systems employ a standard of reasonable doubt, or 'innocent until proven otherwise'. According to this standard, a suspect is to be presumed innocent in the absence of any evidence to the contrary. In this case, the a priori assumption that the suspect is innocent shifts the burden of proof onto the prosecuting agency, thereby protecting individuals from groundless accusations (in theory).

Turning the burden of proof back onto the opponent is often an effective (and sometimes humorous) way to call an opponent out on an argumentum ad ignorantiam. In some cases, an argument from ignorance can be a sign that the two parties are not relying on the same threshold of evidence, or that they are relying on different a priori assumptions. These assumptions and thresholds may merit a debate of their own in these instances.

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D2) Argumentum ad Verecundiam -- Argument by Authority

No one person can legitimately claim authoritative expertise in all fields of human inquiry. Consequently, we all rely on so-called 'experts' to provide input on topics about which their knowledge is authoritative. To the extent that these experts, or more appropriately 'specialists', are providing input on a topic that they possess knowledge of, this reliance on specialized expertise is reasonable. While such expertise may not guarantee infallibility, the opinion of a specialist may be considered superior to that of a layperson when the rendered opinion falls within the topic of the specialist's expertise. The fallacy of argumentum ad verecundiam, or the argument by respect, occurs when the opinion given by the specialist regards a topic outside the specialist's realm of expertise. The following example depicts a common example of ad verecundiam in advertising.

Celebrity: Hello, I'm Mr. U. You may remember me from such popular television shows as 'The B-Team' or 'Mr. U In Charge'. Today, I'm here to tell you about the importance of ethanol. Ethanol is the solution to our energy problems. Call your federal legislators and tell them that Mr. U said to start putting ethanol in your gas tank. It'll be one of the smartest calls you make--I guarantee it!

Example 9. A fictitious celebrity endorsement of ethanol. Although Mr. U may be recognisable as a celebrity, his endorsement of ethanol is completely meaningless in the absence of any evidence that he is somehow an authority on the matter. This appeal to an authority that has no expertise to offer on the topic is an example of argumentum ad verecundiam.

Authoritative knowledge is not fixed, however, and anyone is (at least theoretically) capable of becoming an expert in any field. A politician, for instance, may devote enough effort and study into the topic to become a reliable authority on climate change. Conversely, someone who is now an authority in his field may not still be an authority in the future. Moreover, the opinion of an authority can always be challenged by stronger evidence, better arguments or the contrary opinion of an equally qualified authority. This is why wisdom advises against relying too heavily on expert opinions.

Perhaps the most logical way to confront the use of argumentum ad verecundiam is to ask your opponent to establish the credentials of the expert, and to explain how those credentials lend any credibility to the expert's opinion on the topic being debated. Do not resort to 'finding your own expert' unless you genuinely believe that such an opinion is critical to your argument. Few things are more dull than watching two people hurl a bunch of other peoples' opinions at each other.

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D3) Non Causa Pro Causa -- Questionable Cause

The fallacy of the Questionable Cause, or Non Causa Pro Causa (Latin, 'non-cause for cause') is a claim that a specific causal relationship exists between two things that is not supported by the evidence available. The non causa pro causa fallacy can take several different forms, of which we will examine three of the most common.

'Correlation does not equal causation' is a common mantra in the sciences that is meant to reinforce the fact that a statistical correlation between two events does not establish a causal relationship. This mantra is important to the sciences because complex systems can be difficult to replicate in a standard experimental format, so correlations are much easier to identify in multidimensional datasets than are causal relationships. The fact that events A and B tend to occur together, however, does not offer any reason to conclude that A causes B, or vice versa. An equally plausible explanation is that both A and B are actually caused by C, or that A through Y are all caused by Z. In the absence of any explanatory basis, concluding that a correlation between two events translates into one causing the other is an instance of cum hoc, ergo propter hoc (Latin, 'with this, therefore because of this').

The fallacy of post hoc ergo propter hoc (Latin, 'after the fact, therefore because of the fact') is a very similar form of non causa pro causa that basis the causal connection on the temporal correlation between the factors. Both cum hoc and post hoc occur frequently in the media and in political campaigns, and are also probably responsible for many contemporary and classical superstitions. Our tendency to slip into this mode of thinking seems to stem from our mind's efforts to interpret the world in terms of cause-and-effect relationships. Such explanatory comprehensions are essential to our ability to fulfill resource requirements, but can lead to detrimental behaviors when our understanding of the causal chain is flawed. Instances where the outcome is almost entirely outside a person's control seem to lend themselves to post hoc, ergo propter hoc, as the following fictitious example of a very believable conversation prior to a major sporting event demonstrates:

Dikaiapolis: Hey, what's with the jersey? You've been wearing that thing all week--are you trying to get Helena to dump you again?

Hegestratos: No, this is my special jersey! If I don't wear it for a full week before every Spartan game, they'll loose the game.

Dikaiapolis: So that game they lost to the Polynesians while their coach was in prison...

Hegestratos: Helena dragged me to a fancy dinner with her parents that week, and she hid my jersey.

Example 10. An example of post hoc ergo propter hoc in athletics. While we may applaud Dikaiapolis' loyalty to his team (although certainly not his hygiene), most rational people would agree that the outcome of a sporting event is almost certainly not determined by one fan's apparel.

Post hoc ergo propter hoc is a form of non causa pro causa because it provides no explanation as to how the first event could have caused the second. As with cum hoc, the co-occurrence of two events may be entirely coincidental, both events may be triggered by another external factor, or one may actually be causing the other. Without more information, a basis to conclude anything more about their relationship is absent. While such faulty reasoning can lead to amusing conclusions when applied to trivial issues like sporting events or gambling, the conclusions can be much more dangerous when applied to important issues such as medicine, criminal justice, foreign policy or scientific studies. While a temporal succession may allow you to establish a correlation, a causal relationship cannot be asserted in the absence of a connecting mechanism.

Another common form of non causa pro causa is the aptly-named slippery slope fallacy. The slippery slope fallacy asserts that any change from the status quo in a given direction will have a cascading effect, ultimately leading to an undesirable outcome (hence the analogy of balancing precariously on a slippery slope). If the person making the claim can offer a reasonable chain of possibilities linking the initial change to an undesirable outcome, then the argument is not a slippery slope fallacy. If the person making the claim supports it with one of the two possible lines of reasoning, then the appeal to the slippery slope is not fallacious, but is a reasonable argument:

  1. Once the initial change occurs, following changes are more likely to follow a path to the undesirable outcome than a path to a desirable outcome or back to the status quo
  2. The initial change establishes a precedent that can be used to justify further changes in an undesired direction

An appeal to the slippery slope becomes fallacious when the person proposing it fails to explain how one change will cascade into a series of unwanted events. As with post hoc ergo propter hoc, the absence of a causal explanation invalidates the argument (although not necessarily the conclusion). Discussions of policy issues are excellent places to find slippery slope arguments. Consider the following example, which I paraphrase from a comment on an article about the recent overruling of California's ban on gay marriages:

I can't believe the Court did this. What's this world coming to? Pretty soon, we're going to have people marrying their pet dogs and cats!!

Example 11. A rather glaring example of the slippery slope fallacy. The author of this comment gave no explanation of how the legalization of homosexual unions creates a precedent for interspecies unions.

All three forms of the non causa pro causa fallacy discussed above share the same general error of assuming that one event or action causes another without supplying any rational explanation of why or how this occurs. Consequently, these arguments may support certain conclusions, but not the ones to which they are attached. Pointing this out is often the most effective way to respond to a non causa fallacy. Ask your opponent for a more detailed explanation of the path he took from the initial point that you are discussing to the conclusions he presented. If he is unable to reasonably link the conclusion to the issue, then he has provided no reason to accept his conclusions.

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D4) Converse Accident -- Hasty Generalization

Converse Accident and Hasty Generalization both involve improper extrapolation from specific examples to general principles. In the case of a hasty generalization, the number of samples is too small to justify a general conclusion, while the samples in Converse Accident are the exception to the general population, and therefore inappropriate candidates for generalization. These two fallacies are not mutually exclusive--in fact, one arrives at a Converse Accident either through a Hasty Generalization or a biased sampling.

A Hasty Generalization is exactly what it's name implies: an inductive principle drawn from an insufficiently large number of samples. In many instances, the sample population will be obviously too small to warrant the generalization. In some cases, however, the quantity that constitutes a sufficient number of samples may not be readily apparent. This is particularly problematic when the size of the general population is entirely unknown, or when very few samples are available. Such instances will increase the uncertainty of the generalization and weaken the strength of any argument derived from it. While increasing the number of samples before generalizing any principles is the best way to avoid a Hasty Generalization, and carefully qualifying generalizations with their supporting examples allows your audience to evaluate your conclusions independently.

Because a Hasty Generalization is drawn from a very small population, finding an example that contradicts it is usually rather easy. The following example is based on a censored version of my recollection of a conversation about undocumented workers at an acquaintance's otherwise painfully boring dinner gathering.

Diner 1: Illegal immigrants are stealing all the jobs from honest, hard-working Americans!

Diner 2: Interesting. Why do you say that?

Diner 1: A friend of mine was fired from his job with a landscaping crew. When he went in to pick up his last check two weeks later, some foreigner was running his mower.

Diner 2: And so you conclude that this is a national trend?

Diner 1: Yeah---why?

Example 12. In this example, Diner 1 has committed a Hasty Generalization by assuming that, because her friend lost his job to an (allegedly) 'illegal immigrant', all citizens are losing their jobs to undocumented workers. Note that while the delivery of Diner 2's response with a hefty dose of sarcasm deflated the argument substantially, it did not necessarily invalidate the conclusion.

The sample population of one in the above example is hardly large enough to validate any conclusions about the effects of undocumented workers on citizens' employment prospects. People as a whole tend to be rather difficult to generalize, and generalizations based on socio-economic and ethnic traits are even more likely than others to exhibit frequent exceptions. In this particular case, the claim that an undocumented worker 'stole' a friend's job would be somewhat difficult to disprove. If the company hired the said worker without telling her that she was replacing a more highly paid native worker, is the worker still stealing the job? Moreover, if the worker has no control over the fact that she receives a lower rate of pay than a native worker, can she really be said to be responsible for "stealing" the job? Although these and many other factors complicate the accuracy of Diner 1's argument, its validity is undermined by the failure of Diner 1 to obtain a sufficient sample size before making his argument.

If we were to modify some of the situations surrounding example 12---we'll assume that, in this hypothetical universe, companies do not actively encourage workers to enter another country illegally for work, that said companies face harsh penalties for hiring undocumented workers, that Diner 1's friend has a history of tardiness, debauchery and truculence, and that the company doing the firing was in a desperate financial situation---we could turn Diner 1's argument into an example of a 'Converse Accident'.

In a Converse Accident, the generalization is drawn from the exceptional cases rather than those more indicative of the general population. In addition to an insufficient number of samples, a Converse Accident can also result from biased sampling (e.g. relying solely on data collected from low-income areas to estimate national crime statistics, using only wintertime temperatures to argue against an increase in the planetary climate). Admittedly, no scientific survey is ever entirely accurate, and practical necessity frequently forces us to generalize from incomplete information. However, these limitations do not excuse us from trying our best to recognize potential or actual sources of bias and basing our inductive theories on as complete a sample as we can realistically acquire. While the criteria to establish what qualifies as a sufficiently representative sample can and frequently does vary considerably, once it is established that a conclusion has been drawn from insufficient or exceptional circumstances, that conclusion can be said to inaccurately reflect the general system and the argument supporting it can be considered invalid.

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P) Fallacies of Presumption

Every argument rests on certain a priori assumptions that either all the interested parties have agreed to hold as true or stem from basic or common principles that we consider granted (e.g. our sensory experiences are usually reliable, the sun will rise tomorrow, a thing cannot simultaneously be its self and its antithesis). When these assumptions are reasonable, the practice is valid. In some instances, however, an argument is constructed on an unjustified presumption. In such cases, the argument is a Fallacy of Presumption. Such a fallacy may have a valid link between the premises and the conclusion, but the foundation upon which the premises rest is not valid. Almost any Fallacy of Presumption may be countered by simply pointing out the hidden assumption that your opponent (intentionally or unwittingly) is attempting to slip into the debate.

P1) Fallacy of Accident

The Fallacy of Accident is the counterpart to the Converse Accident described above. Whereas the Converse Accident draws a generalization from exceptional cases, the Accident applies the generalization to the exceptional circumstances. Almost every generalization has its share of reasonable exceptions that should be considered when attempting to apply the generalization to an individual case.

As a general rule, mammals are viviparous (they incubate their offspring internally and give birth to developed young rather than developing embryos in protective eggs). If, however, I were to follow a platypus (Ornithorhynchus anatinus) in hopes of seeing it give birth, I would be sorely disappointed (not to mention in a fair bit of pain if the male happened to notice me). The platypus is an exceptional 'egg-laying, venomous, duck-billed, beaver-tailed, otter-footed mammal'(Quoted from the Wikipedia entry on the platypus) that belongs to a group of monotremes that descended from an early branching of the mammalian family tree and persisted as part of Australia's (and its surrounding islands') unique evolutionary heritage. Although it stands out in relation to other mammals, the platypus fits in well with Australia and New Zealand's unique flora and fauna.

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P2) Plurium Interrogatum -- Complex Question

The phrase 'plurium interrogatum' translates from Latin into 'of many questions', and it refers to a fallacy that embeds the illegitimately presumed premises inside the question itself. This fallacy is also sometimes referred to as a 'complex' or 'loaded' question. It is one of the most common of the Fallacies of Presumption, and it is often used to intentionally conceal the illegitimate premise.

To some extent, any query rests on a certain number of premises. If I were to ask, "What time do you plan to wake up tomorrow?", I am assuming that we both agree that there probably will be a tomorrow, and that you plan to wake up at some point tomorrow. When the question is based on premises that both parties agree on, it is a valid question. If, however, the party asking the question were to slip a premise into the question that the the party answering does not agree is valid, then the question is 'loaded' with an invalid premise, and is therefore fallacious. Such questions are popular in political debates and courtroom dramas.

Attorney: Dr. Green, you just testified that you recommended that the planning commission vote against approving the plans to develop the Happy Mallard Wetlands into a Maulwart Discount Shopping center on the grounds that it would eliminate Fallmeadow's last remaining wetlands. Is that correct?

Witness: Yes, that is correct.

Attorney: Dr. Green, are you really prepared to deny the Fallmeadow community access to food, clothing, medicine and utilities just to save your precious little swamp?

Witness: Wait a minute, I nev---

Attorney: I asked you a yes-or-no question, Dr. Green!

Example 13. An example of plurium interrogatum. In this case, the Attorney is loading the assumption that the only way to provide necessary supplies to the community is by building a 'Maulwart Discount Shopping' center on top of the Happy Mallard Wetlands (the names are completely fictitious, and any resemblance to the names of real institutions is strictly coincidental, by the way---honestly).

The most effective way to challenge a plurium interrogatum is to highlight the invalid assumption and then refute it. In the above example, Dr. Green could turn the tables on the Attorney by asking her whether she is prepared to contend that building that particular market on top of the wetlands is truly the only way to supply the town. Someone asking a deliberately complex question has no right to demand a 'yes-or-no' answer, although that won't necessarily stop him from trying to bully his victim into giving one. Calling out a complex question is not 'side-stepping' the issue, either---in fact, by bringing the unsupported presumption into the open and challenging it, you are actually moving the debate closer to its intended topic. Having never been called upon to provide witness or expert testimony in court, I cannot guarantee that Dr. Green would not be held in 'contempt of court' for refusing to answer the question as-phrased, but I'd be surprised if she was.

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P3) Petitio Principii -- Begging the Question

The circular logic of assuming the truth of a conclusion and using it with slightly different wording to validate the truth of the same conclusion is a fallacy known as 'Petitio Principii', or begging the question. While such a fallacy may seem readily detectable, a cleverly worded petitio principii fallacy can slip past even the most diligent logicians at times. Such fallacies seem to occur more frequently in debates that involve metaphysical or eschatological issues--issues with premises that do not lend themselves to empirical verification.

A petitio principii fallacy is flawed not because it rests on an a priori assumption, but because this assumption also happens to be the one that the individual using it is trying to prove. Consider the following argument used by altogether too many evangelicals regarding the veracity of the Judeo-Christian Scriptures:

Evangelist: The Holy Scriptures are infallible and perfectly accurate.

Skeptic: How do you know that?

Evangelist: Because they say so. In Matthew 24.35 Jesus says, 'Heaven and earth will pass away, but my words will not pass away.', and Proverbs 30.5 says, 'Every word of God proves true...'

Skeptic: So what you're telling me is that the Bible is accurate because it says it's accurate? And you want me to take you seriously?

Example 14. An unfortunate example of petitio principii. While good reasons to believe that different religions' sacred texts are infallible do presumably exist, the fact that they say they are so is not one of them.

As with the other fallacies of presumptions, the best counter to a petitio principii is to point out the repeated assumption. This at least works well when the fallacy is committed unintentionally, as well as in circumstances where the debate is being observed by a number of onlookers who will help to arbitrate.

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P4) False Dilemma

A dilemma, according to The Oxford Modern English Dictionaryis a situation in which a choice has to be made between two equally undesirable alternatives. The fallacy of the false dilemma is an attempt to convince you that such a situation exists by surreptitiously eliminating alternative outcomes. While the name implies that only two options are available, this fallacy can be generalized to any situation where alternatives are illegitimately removed from the dialogue (perhaps a more appropriate moniker would be 'Fallacy of the Excluded Middle'). Often, the false dilemma takes the extreme ends of a range of options and juxtaposes them in a single set of alternatives. Consider the following excerpt from an article from MSNBC about a statement made by Pope Benedict XVI:

“They are presented as alternatives that exclude each other,” the pope said. “This clash is an absurdity because on one hand there is much scientific proof in favor of evolution, which appears as a reality that we must see and which enriches our understanding of life and being as such.”

He said evolution did not answer all the questions: “Above all it does not answer the great philosophical question, ‘Where does everything come from?’”

Example 15. In a discussion about the 'evolution vs. creation' debate in the U.S. and Germany, Pope Benedict XVI points out that the two ideas are not necessarily mutually exclusive. Forcing someone to accept evolution or creation creates a false dilemma, as the one does not inherently preclude the validity of the other. From Pope: Creation vs. evolution clash an 'absurdity', MSNBC News Services, 25 July 2007. http://www.msnbc.msn.com/id/19956961/.

Although it is called a false dilemma, this fallacy does not require that both alternatives be equally undesirable. The fallacy refers to any instance where the number of options is illegitimately reduced. It is included in the category of presumption because it stems from a disagreement over unstated premises in the argument that circumscribe the range of acceptable alternatives. The party presenting the dilemma is relying on premises that the alternate party either is unaware of or does not consider valid. The best way to resolve such a situation is to attempt to identify the unstated assumption and then debate it reasonably.

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A) Fallacies of Ambiguity (Sophisms)

Fallacies of Ambiguity, or Sophisms, occur when a term of phrase has one meaning in a premise, and a different meaning in the conclusion. Linguistic puns would fall into this category if they were ever used intentionally (or otherwise) in an argument. Deliberate attempts to obscure an argument with confusion are usually rather obvious, but unintentional ambiguities can be more subtle. These fallacies can usually be rectified fairly easily by simply asking the other party to explain her argument more clearly or with an alternate wording.

A1) Equivocation

Designers of the English Language appear to have practiced a bizarre form of linguistic economy--i.e. several individual words have multiple completely independent (or only vaguely related) meanings. A file can hold important documents or round out your fingernails, a case can be argued in court or house a collection of jewelery and a moon can orbit a planet or get you arrested for indecent exposure. Puns are deliberate attempts to confuse alternate meanings of words for comic effect, and are usually harmless. In a debate, however, the deliberate or accidental confusion of meanings is a logical fallacy known as 'equivocation'. In many cases, the equivocation is obvious enough to be readily identified by someone who examines the chain of reasoning closely.

Particularly in more complex arguments, equivocation can slip into a series of premises undetected, and remain so for quite a while. In a teaching on his thoughts about evolution, Greg Koukl, of Stand to Reason, accuses evolutionists of equivocation:

Evolution has at least three different definitions. Definition 1 is change over time, 2 is the Special Theory of Evolution, and 3 is the General Theory of Evolution. If I just say that I disagree with evolution, someone could assume that I'm arguing that things don't change over time, when in reality I'm trying to say that I don't believe the 'Molecules to Man' hypothesis.

Example 16. Greg Koukl contends that discussing evolution without clarifying which type your referring to is equivocation. Although---in my experiences anyway---scientists frequently group all three of Koukl's forms of evolution together as a sort of shorthand way of referring to the whole evolutionary process and its mechanisms, it does seem to make sense to clarify which aspect of evolution you're referring to when debating the validity of 'evolution'. As this suggests, there's also the distinction between evolution itself, which is simply defined as change over time, and the mechanisms driving evolution, which are believed to include interspecific competition, genetic mutation, symbiosis, and ecological drift. Example paraphrased from Koukl's Stand to Reason.

The key to identifying an instance of equivocation and to avoiding it yourself is to examine the wording of the premises and the conclusions to see whether they are open to alternate interpretations. If so, then attempt to clarify the intended interpretation by further qualifying the statement or by an alternate word choice, or ask the person making the argument to do the same.

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A2) Amphiboly

The fallacy of amphiboly stems from a misuse of grammatical principles in the formation of the argument. Such fallacies are easier to identify when they occur in print, although they are not limited to this medium. Amphiboly is more likely to lead to confusion and to damage the credibility of the person making the argument than it is to result in an invalid conclusion. The disturbingly popular reactionary political commentator Anne Coulter provides an interesting example of amphiboly in her opinions on the best way to handle terrorism:

We should invade their countries, kill their leaders and convert them to Christianity.

Example 17. I'm really not sure how one goes about converting a dead leader to Christianity. Much of the confusion in this instance of amphiboly stems from the absence of a qualifier for who 'they' refers to, and confusion about whether the comma was omitted before 'and' because it is attached to 'leaders' or because it is the last item in a list. From Coulter (2001) This Is War: We should invade their countries. National Review. Available from the Web Archive at http://web.archive.org/web/20010914225811/http://www.nationalreview.com/coulter/coulter091301.shtml.

If the author is not available, amphiboly can be difficult to clarify when it occurs in print. When a spoken statement is ambiguous, requesting clarification from the speaker is usually effective and a good way to avoid committing a straw man fallacy.

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A3) Accent

The fallacy of accent occurs when the wrong word or phrase is stressed, and so takes place primarily in spoken arguments. The message communicated by a phrase spoken in English, as with several other languages, is highly sensitive to the tone of the speaker and the placement of emphasis on individual words. Ironic or sarcastic statements are particularly dependent on the placement of stresses in the statement. A speaker can inadvertently or intentionally change the meaning of her entire statement by simply moving the emphasis to a different word. The following example illustrates this by shifting the emphasized word in a stranded motorist's thanks to a police officer. The emphasis was denoted by italics, until I discovered that the current template italicizes the whole darn thing; now, the emphasis is denoted by strong tags:

It was so good of you to help me when my car broke down!
-You have performed an act of kindness

It was so good of you to help me when my car broke down!
-Your heart was in the right place, but you're getting on my nerves now

It was so good of you to help me when my car broke down!
-I'm glad that you were the one who decided to help

It was so good of you to help me when my car broke down!
-As opposed to shooting me in the head and taking my wallet.

It was so good of you to help me when my car broke down!
-Instead of helping the guy with flames and loud screams coming from his vehicle 20 meters down the road

It was so good of you to help me when my car broke down!
-Rather than waiting until I gave up and hitch-hiked my way home

It was so good of you to help me when my car broke down!
-I just left my neighbor's car on the side of the road when it ran out of gas on my last week

It was so good of you to help me when my car broke down!
-Where were you when my Abrams M1 died in the middle of the desert?

Example 18. The same sentence carries a very different meaning when the accent shifts to another word.

A non-vocal version of Accent does tend to appear in email and text messages. In these cases, the problem is the absence of an indication of where the emphasis belongs. Consequently, a message intended to communicate gratitude instead starts a conflict, and soon both parties begin to resort to advanced textual criticisms in their attempts to decipher each other's ambiguous messages. I believe that this inability to communicate the emotional context via text is largely responsible for the proliferation of 'smileys' and other creative ASCII constructs.

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A4) Composition

A Fallacy of Composition inappropriately attributes attributes of individual components of a group to the group as a single entity. The collective can either be a group of similar elements, or an entity that the elements are components of. In the former case, the collective contribution of the individual elements may accumulate in the group, reversing the status of the element. For instance, a single feather has very little mass, and therefore very little weight. Even with their low individual weight, a tonne of feathers would be virtually impossible to lift without mechanical assistance. In the latter instance, the fallacy stems from the outcomes of a system's components are as much defined by their interactions as by their individual attributes. Placing five very gifted scientists in a single research laboratory does not necessarily translate into better research, for instance. The skills of the researchers must be combined with an ability to co-operate and compliment each other; otherwise the lab will have a greater likelihood of performing more poorly than other labs. Similarly, although a corporation may be composed of several moral agents who operate under certain ethical constraints, a corporation itself is not a moral agent, and therefore should not be reasonably expected to exhibit self-imposed ethical restraint. This is why regulation most be imposed by an outside entity, usually in the form of legislative constraints.

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A5) Division

The Fallacy of Division also neglects the synergistic nature of systems produced by interacting components. It is the opposite of Composition in that the errant reasoning proceeds from the attributes of the whole to the attributes of the individual parts. Like Composition, Division also has two forms, one of which refers to groups of similar entities, and the other to a single entity composed of multiple elements. Following the discussion of Composition, assuming that, because corporations are essentially amoral entities, any individual member of a corporate body is also amoral is as fallacious as assuming a corporation of moral agents will itself be moral. The science of reductionism followed this line of reasoning from Descartes to the modern era. Scientists believed that if they could identify and understand each component of a complex system, they could fully comprehend and manipulate that system. While such methodical inquiries brought us many new discoveries, the many ecological crises we now face have forced a paradigm shift that acknowledges that complex systems may exhibit characteristics not found in their individual components.

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4. Conclusion

I had originally intended for this article to be a brief list of fallacies. Then, I realized that just listing the fallacies was rather pointless, and that I ought to add some explanations. Explanations tend to be rather cloudy without examples, however, and I soon found myself adding those. Finally, I decided that some advice on responding to and avoiding these fallacies would be helpful, and so the article continued to evolve. I have been working on this off-and-on for several months, and so I apologize for any abrupt breaks in the flow of the text. Now that the article is written, I will slowly revise and expand on it as I notice areas that need work or clarification. I also welcome feedback, particularly input on whether you found this article helpful and any suggestions you may have for improvements. I hope that this article will help you to think critically about arguments presented to you, and that just maybe you're considering learning a little bit more about logic and reasoning.

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5. See Also

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6. Recommended Texts

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