Our brains have evolved in such a way that thinking around corners is something we do naturally.  We are by nature problem solvers and we are always trying to spot the patterns in the world around us - in fact we are happier with a pattern than without one even if we have to make it up because no such pattern exists.  We can fall into the trap of making false arguments which don’t make sense - we will literally think around corners sometimes.

“Logical errors are, I think, of greater practical importance than many people believe; they enable their perpetrators to hold the comfortable opinion on every subject in turn.”

Source: Bertrand Russell

“There's a mighty big difference between good, sound reasons and reasons that sound good.”

Source: Burton Hillis

Here are a few examples of thinking round corners, how to spot them and hopefully how to straighten out your own thought processes a little.

Please keep in mind that throughout this piece I am talking about thoughts and arguments relating to factual claims, not subjective feelings or value judgements. You may prefer Mozart to Beethoven, but no matter how straight you think and talk you can’t prove you are right or wrong.  It is therefore very helpful in life to be able to identify when we are thinking and talking about facts and logic as opposed to aesthetic opinion or a moral choice. Such a thought is a way of coming to a conclusion or making a case or outlining an argument.

Structure of a Logical Argument.

Whether we are consciously aware of it or not, thoughts of this type all follow a certain basic structure.

Premise 1: If A = B,

Premise 2: and B = C

Logical connection: Then (apply principle of equivalence)

Conclusion: A = C - This is my idea of thinking straight.

In order for a conclusion to be considered valid all the premises of an argument must be true, and the logical connection must be valid.

By “valid” we specifically refer to such conclusions, because a conclusion may still be “true” even if it is not valid. This is because it is possible to use wrong information, or faulty logic to reach a conclusion that happens to be true.   You can do the math wrong but still get the right answer sometimes.  An invalid argument does not necessarily prove the conclusion false. Demonstrating that an argument is not valid, however, removes it as support for the truth of the conclusion.

A key skill for thinking straight is therefore being able to correctly identify the components of the  argument.  This enables us to examine both our own arguments and those of others and critically analyse 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 valid 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 invalid because the premise – no transitional fossils – is

false. In fact there are actually tons (in every sense of the word) of transitional fossils.

A second type of premise error occurs when one or more premise 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 analysing 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 rationalisation.

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 realise they are using different assumptions as premises, then at least they can “agree to disagree.” They will realise 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. 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 palaeontologist 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 descendent species; or it can be temporally between two species, the descendent 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. But if they fill a morphological gap in known species, they provide evidence of an evolutionary connection, and therefore qualify as transitional.

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.

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 marvellous 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.

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 valid argument 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 is a list the most common logical fallacies, with examples of each. It is important to note that many claims may contain multiple logical fallacies at once. Also, some types of logic may fit into different types of fallacies simultaneously.

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 many of the fallacies listed below are also non-sequiturs but are an identifiable and common type.

Subtype of Non-Sequitur: Magical Thinking

Magical thinking is perhaps the most common type of non-sequitur. The logical connection in these fallacious arguments are often a vague magical principle not based upon logic or evidence.

For example, Feng Shui proponents might argue that it is better to place your bed in a certain position within your bedroom so that luck will flow into your home.

This is the bagua (or pa kua) of the Yi Jing (Book of Changes) is an octagonal diagram that is used in feng shui analysis.  There is no scientific evidence or reasoning behind it - it is a classical example of Magical Thinking. 

To help make it clear what I mean by “scientific evidence” here’s a nice quote;

“Science is simply common sense at its best; that is, rigidly accurate in observation, and merciless to fallacy in logic.”

Source: Thomas Henry Huxley

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 emphasising 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 considered valid 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.

The argument from authority, or appeal to authority, has many potential subtypes, all of which invest authority in a particular group or situation. In the broadest sense this logical fallacy assumes that because a person or group possesses some positive quality (such as authority), their claims are true. Below are some examples of different types of positive qualities worth specific mention.

Subtype of Argument from Authority: Appeal to Common Belief

This fallacy is the argument that a claim must be true because many people believe it. It ignores the possibility, demonstrated frequently throughout history, that the majority can be completely wrong. The popularity of an idea or claim is often based upon features other than logic or evidence.

Subtype of Argument from Authority: Appeal to Impending Acceptance

I consider this to be a subtype to the argument from authority, because it attempts to invoke the authority of future belief and acceptance. Many pseudo-sciences, such as creationism, ESP, and UFO-logy, claim that broad acceptance is right around the corner. This is a logical fallacy (the argument from authority) coupled with an assumed premise (that of future acceptance).

Subtype of Argument from Authority: Appeal to Virtue or Sincerity

This is the argument that a person or group possesses a virtue and therefore their claims must be true.

For example, alternative medicine proponents often cite that a particular practitioner is very sincere and caring, and therefore claims for the efficacy of their treatment should be believed.

This is Samuel Hahnemann, the father of homeopathy who held his views very sincerely as far as we know.

I think that Richard Dawkins, Professor of the Public Understanding of Science at Oxford, puts it across well in his definition of alternative medicine, based not on the sincerity of the practitioners but on evidence: "alternative medicine is defined as that set of practices which cannot be tested, refuse to be tested, or consistently fail tests. If a healing technique is demonstrated to have curative properties in properly controlled double-blind trials, it ceases to be alternative. It simply...becomes medicine." He also states that "There is no alternative medicine. There is only medicine that works and medicine that doesn't work.

Also, a credulous ghost hunter might argue that an eyewitness who claimed to have seen someone levitate three feet off their bed should be believed because “why would she lie?”.

Subtype of Argument from Authority: Argument from Conspiracy or Anti-Authority

This is the converse of the argument from authority, and basically states that a claim is false because it is held and promoted by an authority. This occurs often in the context that the official government position must be false because it’s the official government position. This could also be considered a subtype of ad-hominem logical fallacy, arguing that the government must be wrong because they habitually lie or engage in cover-up conspiracies.

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