Arguing is one of those things most people do but few people do well. Many do not understand what a logical argument even is or how to do it correctly. Yet arguing is an essential skill of critical thinking. How we argue reflects how we think, how we evaluate our own conclusions, and how we challenge the beliefs of others.

Even the very purpose of arguing is often misunderstood. I have arguments almost every day. This does not mean I verbally fight with others on a daily basis, but rather I have discussions that involve either attempting to convince another of a specific conclusion, or resolving different conclusions on a factual matter. In most of the arguments that I find myself the other person has staked out a position and they defend it jealously, as if they were a high-paid lawyer defending a client. This adversarial approach, however, is not constructive. Rather, the parties of an argument should be trying to find common ground, and then proceed carefully from that common ground to resolve any differences.

The beauty of a logical argument is that it is, well… logical. It is, in a way, like mathematics. In math 1+1 must =2. If there is a disagreement about this, it can be resolved objectively and definitively. If two people doing the same math problem come up with different answers, how should they respond? Should they each defend their answer at all costs. Or, should they exam each other’s solution to see if one, or both, might contain an error, and then resolve the error to see what the correct answer is?

Likewise, if two people have come to different conclusions about a factual claim, then one or both must be wrong. Both cannot be correct. That means that one or both must have made an error in the arguments they used to come to their conclusions. The two parties should work together to examine their arguments and resolve any errors.

Keep in mind, this only works if the arguments are about factual claims, not subjective feelings or value judgments. There is no objective way to resolve a difference of opinion regarding aesthetics, for example. If you prefer Mozart to Beethoven, there is no way to prove that with facts or logic. It is very helpful, however, to identify when a conclusion contains an aesthetic opinion or a moral choice. It avoids arguing endlessly over an issue that is inherently irresolvable.

An excellent example of this is the abortion debate. Ultimately, all arguments over abortion come down to a personal moral choice: which should have greater value, the mother’s right to make choices regarding her own body, or the unborn fetus’s right not to be killed. All attempts to resolve this objectively have resulted in further arguments that are dependent upon value judgments, for example: at what point at or after conception does an embryo or fetus become a person? Also, how does the fetus’s total biological dependence upon its mother affect their respective rights?

Structure of a Logical Argument

Whether we are consciously aware of it or not, our arguments all follow a certain basic structure. They begin with one or more premises, which are facts that the argument takes for granted as the starting point. Then a principle of logic is applied in order to come to a conclusion. This structure is often illustrated symbolically with the following example:

Premise1: If A = B,
Premise2: and B = C
Logical connection: Then (apply principle of equivalence)
Conclusion: A = C

In order for an argument to be considered valid the logical form of the argument must work – must be valid. A valid argument is one in which, if the premises are true, then the conclusion must be true also. However, if one or more premise is false then a valid logical argument may still lead to a false conclusion. A sound argument is one in which the logic is valid and the premises are true, in which case the conclusion must be true.

Also it is important to note that and argument may use wrong information, or faulty logic to reach a conclusion that happens to be true. An invalid or unsound argument does not necessarily prove the conclusion false. Demonstrating that an argument is not valid or not sound, however, removes it as support for the truth of the conclusion.

Breaking down an argument into its components is a very useful exercise, for it enables us to examine both our own arguments and those of others and critically analyze them for validity. This is an excellent way of sharpening one’s thinking, avoiding biases, and making effective arguments.

Examine your Premises

As stated above, in order for an argument to be sound all of its premises must be true. Often, different people come to different conclusions because they are starting with different premises. So examining all the premises of each argument is a good place to start.

There are three types of potential problems with premises. The first, and most obvious, is that a premise can be wrong. If one argues, for example, that evolutionary theory is false because there are no transitional fossils, that argument is unsound because the premise – no transitional fossils – is false. In fact there are copious transitional fossils.

Another type of premise error occurs when one or more premises is an unwarranted assumption. The premise may or may not be true, but it has not been established sufficiently to serve as a premise for an argument. Identifying all the assumptions upon which an argument is dependent is often the most critical step in analyzing an argument. Frequently, different conclusions are arrived at because of differing assumptions.

Often people will choose the assumptions that best fit the conclusion they prefer. In fact, psychological experiments show that most people start with conclusions they desire, then reverse engineer arguments to support them – a process called rationalization.

One way to resolve the problem of using assumptions as premises is to carefully identify and disclose those assumptions up front. Such arguments are often called “hypothetical,” or prefaced with the statement “Let’s assume for the sake of argument.” Also, if two people examine their arguments and realize they are using different assumptions as premises, then at least they can “agree to disagree.” They will realize that their disagreement cannot be resolved until more information is available to clarify which assumptions are more likely to be correct.

The third type of premise difficulty is the most insidious: the hidden premise. I have seen this listed as a logical fallacy – the unstated major premise, but it is more accurate to consider it here. Obviously, if a disagreement is based upon a hidden premise, then the disagreement will be irresolvable. So when coming to an impasse in resolving differences, it is a good idea to go back and see if there are any implied premises that have not been addressed.

Let’s go back to the transitional fossil example again. Why is it that scientists believe we have many transitional fossils and evolution deniers (creationists or intelligent design proponents) believe that we do not. This would seem to be a straightforward factual claim easily resolvable by checking the evidence. Sometimes evolution deniers are simply ignorant of the evidence or are being intellectually dishonest. However, the more sophisticated are fully aware of the fossil evidence and use a hidden premise to deny the existence of transitional fossils.

When a paleontologist speaks of “transitional” fossils, they are referring to species that occupy a space morphologically between two known species. This may be a common ancestor, in which case the transitional fossil will be more ancient than both descendant species; or it can be temporally between two species, the descendant of one and the ancestor of the other. But in reality we often do not know if the transitional species is an actual ancestor or just closely related to the true ancestor. Because evolution is a bushy process, and not linear, most of the specimens we find will lie on an evolutionary side branch (an uncle rather than a parent). But if they fill a morphological gap in known species, they provide evidence of an evolutionary connection, and therefore qualify as transitional. For example, archaeopteryx may not be on the direct path to modern birds, but clearly they occupy a space that is transitional between therapod dinosaurs and modern birds and one of their close relatives is a direct ancestor to modern birds.

When evolution deniers say there are no transitional fossils their unstated major premise is that they are employing a different definition of transitional than is generally accepted in the scientific community. They typically define transitional as some impossible monster with half-formed and useless structures. Or, they may define transitional as only those fossils for which there is independent proof of being a true ancestor, rather than simply closely related to a direct ancestor – an impossible standard.

Another hidden premise in their argument is the notion of how many transitional fossils there should be in the fossil record.  They, of course, can always assume an arbitrarily high number to claim that there isn’t enough.

Logical Fallacies

Even when all of the premises of an argument are reliably true, the argument may still be invalid if the logic employed is not legitimate – a so called logical fallacy. The human brain is a marvelous machine with capabilities that, in some ways, still outperform the most powerful of super computers. Our brains, however, do not appear to have evolved specifically for precise logic. There are many common logical pitfalls that our minds tend to fall into, unless we are consciously aware of these pitfalls and make efforts to avoid them.

Humans also tend to use logical short-cuts, called heuristics. These are thought processes that are not strictly valid in their logic, but are true most of the time and therefore are a useful rule-of-thumb as to what is likely to be true. But they get us into trouble when then substitute for valid logic.

Also because, as stated above, there is a tendency to start with desired conclusions and then construct arguments to support them, many people will happily draw upon logical fallacies to make their arguments. In fact, if a conclusion is not true one must either employ a false premise or a logical fallacy in order to construct an argument that leads to that conclusion. Remember, a sound argument (one with true premises and valid logic) cannot lead to a false conclusion. So in order to avoid using logical fallacies to construct invalid arguments, we need to understand how to identify fallacious logic.

Below I will list the most common logical fallacies, with examples of each.

On a side note, I have found many lists of logical fallacies, and they tend to differ along the “lumper vs splitter” spectrum. Many fallacies are really just specific subtypes of a more general fallacy. I have taken a combined approach, listing the main types of fallacies and giving examples of subtypes where appropriate.

Non-Sequitur
In Latin this term translates to “doesn’t follow.” This refers to an argument in which the conclusion does not necessarily follow from the premises. In other words, a logical connection is implied where none exists. This is the most basic type of logical fallacy, and in fact all logical fallacies are non-sequiturs, but are an identifiable and common type.

Argument from authority
The basic structure of such arguments is as follows: Professor X believes A, Professor X speaks from authority, therefore A is true. Often this argument is implied by emphasizing the many years of experience, or the formal degrees held by the individual making a specific claim. The converse of this argument is sometimes used, that someone does not possess authority, and therefore their claims must be false. (This may also be considered an ad-hominen logical fallacy – see below.)

In practice this can be a complex logical fallacy to deal with. It is legitimate to consider the training and experience of an individual when examining their assessment of a particular claim. Also, a consensus of scientific opinion does carry some legitimate authority. But it is still possible for highly educated individuals, and a broad consensus to be wrong – speaking from authority does not make a claim true.

This logical fallacy crops up in more subtle ways also. For example, UFO proponents have argued that UFO sightings by airline pilots should be given special weight because pilots are trained observers, are reliable characters, and are trained not to panic in emergencies. In essence, they are arguing that we should trust the pilot’s authority as an eye witness.

There are many subtypes of the argument from authority, essentially referring to the implied source of authority. A common example is the argument ad populi – a belief must be true because it is popular, essentially assuming the authority of the masses. Another example is the argument from antiquity – a belief has been around for a long time and therefore must be true.

Argument from final outcome
Such arguments (also called teleological) are based on a reversal of cause and effect, because they argue that something is caused by the ultimate effect that it has, or purpose that is serves. Christian creationists have argued, for example, that evolution must be wrong because if it were true it would lead to immorality.

Post-hoc ergo propter hoc
This is perhaps the most common of logical fallacies. It follows the basic format of A preceded B, therefore A caused B, and therefore assumes cause and effect for two events just because they are temporally related (the Latin translates to “after this, therefore because of this”). This logical fallacy is frequently invoked when defending various forms of alternative medicine – I was sick, I took treatment A, I got better, therefore treatment A made me better. This is a logical fallacy because it is possible to have recovered from an illness without any treatment.

Confusing correlation with causation
This is similar to the post-hoc fallacy in that it assumes cause and effect for two variables simply because they occur together. This fallacy is often used to give a statistical correlation a causal interpretation. For example, during the 1990’s both religious attendance and illegal drug use have been on the rise. It would be a fallacy to conclude that therefore, religious attendance causes illegal drug use. It is also possible that drug use leads to an increase in religious attendance, or that both drug use and religious attendance are increased by a third variable, such as an increase in societal unrest. It is also possible that both variables are independent of one another, and it is mere coincidence that they are both increasing at the same time.

This fallacy, however, has a tendency to be abused, or applied inappropriately, to deny all statistical evidence. In fact this constitutes a logical fallacy in itself, the denial of causation. This abuse takes two basic forms. The first is to deny the significance of correlations that are demonstrated with prospective controlled data, such as would be acquired during a clinical experiment. The problem with assuming cause and effect from mere correlation is not that a causal relationship is impossible, it’s just that there are other variables that must be considered and not ruled out a-priori. A controlled trial, however, by its design attempts to control for as many variables as possible in order to maximize the probability that a positive correlation is in fact due to a causation.

Further, even with purely epidemiological, or statistical, evidence it is still possible to build a strong scientific case for a specific cause. The way to do this is to look at multiple independent correlations to see if they all point to the same causal relationship. For example, it was observed that cigarette smoking correlates with getting lung cancer. The tobacco industry, invoking the “correlation is not causation” logical fallacy, argued that this did not prove causation. They offered as an alternate explanation “factor x”, a third variable that causes both smoking and lung cancer. But we can make predictions based upon the smoking causes cancer hypothesis. If this is the correct causal relationship, then duration of smoking should correlate with cancer risk, quitting smoking should decrease cancer risk, smoking unfiltered cigarettes should have a higher cancer risk than filtered cigarettes, etc. If all of these correlations turn out to be true, which they are, then we can triangulate to the smoking causes cancer hypothesis as the most likely possible causal relationship and it is not a logical fallacy to conclude from this evidence that smoking probably causes lung cancer.

Special pleading, or ad-hoc reasoning
This is a subtle fallacy which is often difficult to recognize. In essence, it is the arbitrary introduction of new elements into an argument in order to jerry rig them, or fix them so that they appear valid. A good example of this is the ad-hoc dismissal of negative test results. For example, one might argue that ESP has never been demonstrated under adequate test conditions, therefore ESP is not a genuine phenomenon. Defenders of ESP have attempted to counter this argument by introducing the arbitrary premise that ESP does not work in the presence of skeptics. This fallacy is often taken to ridiculous extremes, and more and more bizarre ad hoc elements are added to explain experimental failures or logical inconsistencies.

Carl Sagan gave perhaps the most famous example of this fallacy in his “invisible, floating, non-corporeal, heatless, dragon in his garage” argument.  Essentially, he claims that there is a dragon in his garage, and then invents a special reason why each test for the presence of the dragon fails.

Tu quoque
Tu quoque translates to “you too.” This is an attempt to justify wrong action because someone else also does it. “My evidence may be bad, but so is yours.” This fallacy is frequently committed by proponents of various alternative medicine modalities, who argue that even though their therapies may lack evidence more mainstream modalities also lack evidence.

Ad hominem
An ad hominem argument is any that attempts to counter another’s claims or conclusions by attacking the person, rather than addressing the argument itself. True believers will often commit this fallacy by countering the arguments of skeptics by stating that skeptics are closed minded. Skeptics, on the other hand, may fall into the trap of dismissing the claims of UFO believers, for example, by stating that people who believe in UFO’s are crazy or stupid.

A common form of this fallacy is also frequently present in the arguments of conspiracy theorists (who also rely heavily on ad-hoc reasoning). For example, they may argue that the government must be lying because they are corrupt.

The term “poisoning the well” also refers to a form of ad hominem fallacy.  This is an attempt to discredit the argument of another by implying that they possess an unsavory trait, or that they are affiliated with other beliefs or people that are wrong or unpopular. A common form of this also has its own name – Godwin’s Law or the reductio ad Hitlerum. This refers to an attempt at poisoning the well by drawing an analogy between another’s position and Hitler or the Nazis.

Ad ignorantum
The argument from ignorance basically states that a specific belief is true because we don’t know that it isn’t true. Defenders of extrasensory perception, for example, will often overemphasize how much we do not know about the human brain. It is therefore possible, they argue, that the brain may be capable of transmitting signals at a distance.

UFO proponents are probably the most frequent violators of this fallacy. Almost all UFO eyewitness evidence is ultimately an argument from ignorance – lights or objects sighted in the sky are unknown, and therefore they are alien spacecraft.

Intelligent design is almost entirely based upon this fallacy. The core argument for intelligent design is that there are biological structures that have not been fully explained by evolution, therefore a powerful intelligent designer must have created them.

In order to make a positive claim, however, positive evidence for the specific claim must be presented. The absence of another explanation only means that we do not know – it doesn’t mean we get to make up a specific explanation.

Confusing currently unexplained with unexplainable
Because we do not currently have an adequate explanation for a phenomenon does not mean that it is forever unexplainable, or that it therefore defies the laws of nature or requires a paranormal explanation. An example of this is the “God of the Gaps” strategy of creationists that whatever we cannot currently explain is unexplainable and was therefore an act of god.

False Continuum
The idea that because there is no definitive demarcation line between two extremes, that the distinction between the extremes is not real or meaningful: For example, there is a fuzzy line between cults and religion, therefore they are really the same thing.

False Dichotomy
Arbitrarily reducing a set of many possibilities to only two. For example, evolution is not possible, therefore we must have been created (assumes these are the only two possibilities). This fallacy can also be used to oversimplify a continuum of variation to two black and white choices. For example, science and pseudoscience are not two discrete entities, but rather the methods and claims of all those who attempt to explain reality fall along a continuum from one extreme to the other. Reducing all factual claims to either pure science or pure pseudoscience would be creating a false dichotomy.

Inconsistency
Applying criteria or rules to one belief, claim, argument, or position but not to others. For example, some consumer advocates argue that we need stronger regulation of prescription drugs to ensure their safety and effectiveness, but at the same time argue that medicinal herbs should be sold with no regulation for either safety or effectiveness.

Reductio ad absurdum
In formal logic, the reductio ad absurdum is a legitimate argument. It follows the form that if the premises are assumed to be true it necessarily leads to an absurd (false) conclusion and therefore one or more premises must be false. The term is now often used to refer to the abuse of this style of argument, by stretching the logic in order to force an absurd conclusion. For example a UFO enthusiast once argued that if I am skeptical about the existence of alien visitors, I must also be skeptical of the existence of the Great Wall of China, since I have not personally seen either. This is a false reductio ad absurdum because he is ignoring evidence other than personal eyewitness evidence, and also logical inference. In short, being skeptical of UFO’s does not require rejecting the existence of the Great Wall.

Slippery Slope
This logical fallacy is the argument that a position is not consistent or tenable because accepting the position means that the extreme of the position must also be accepted. But moderate positions do not necessarily lead down the slippery slope to the extreme. This is common in politics. For example, some opponents to embryonic stem cell research have argued that allowing the use of human embryos in research (even those created for IVF that would otherwise be discarded) would inevitably lead to creating embryos specifically for research, a black market in human embryos, or even the forcible extraction of eggs for such research from women.

Tautology
Tautology is an argument that utilizes circular reasoning, which means that the conclusion is also its own premise. The structure of such arguments is A=B therefore A=B, although the premise and conclusion might be formulated differently so it is not immediately apparent as such. For example, saying that therapeutic touch works because it manipulates the life force is a tautology because the definition of therapeutic touch is the alleged manipulation (without touching) of the life force.

The Moving Goalpost
A method of denial arbitrarily moving the criteria for “proof” or acceptance out of range of whatever evidence currently exists. If new evidence comes to light meeting the prior criteria, the goalpost is pushed back further – keeping it out of range of the new evidence. Sometimes impossible criteria are set up at the start – moving the goalpost impossibly out of range -for the purpose of denying an undesirable conclusion.

Conclusion

This list of logical fallacies is certainly incomplete. A thorough treatment of this topic is more appropriate to a rather large book than a blog post. However, applying this basic approach to arguing would, in my experience, vastly improve the arguing style of most people.

Just remember to apply these rules to yourself first and foremost.

Note: This is an updated version of an article I have previously written. The original version is currently inaccessible as the NESS website is being moved to a new host and updated. However, since I have tried to make logic central to NeuroLogica I thought this article should also have a home here. And it was a good opportunity to significantly update the article.