This content of this blog is adapted from my lecture on Cognitive Bias in Decision Making, for the module Cognition and Emotion. I present this lecture to third year Psychology students at the University of Roehampton, London.

The Structure of an Argument

How to sort good information from bad!

Just like visual illusions, our understanding of the world around us can be incorrect, despite appearing completely accurate or despite our feeling our conclusion must be true because it ‘just feels right’. Knowing we make mistakes about our interpretation of the world is not enough though. While it is important to know you have made an error in reasoning, this alone does not help us to sort out way through the mass if irrelevant information we are presented with on a daily basis. Understanding how we make these errors in our decisions, or conclusions, helps to provide us with an insight into our decision making process. This awareness, not only reduces the likelihood of making these errors again, but increases our chances of detecting the same errors when they are made by others. By knowing what to look for when evaluating our own thoughts and beliefs, or the thoughts and beliefs of others, provides us with the power to make better choices based on the information at hand, rather than basing our decisions on our feelings or simply ending up confused by what might appear to be contradictory or convoluted information. This awareness of our feelings and thought processes has played a substantial role in our understanding of the world throughout history and is the very reason why our species has advanced technologically so much more in just the last 100 years, compared to the whole of the previous 10,000.

 These thoughts, feelings, and beliefs shape how we understand the present and make decisions for the future and are based on ‘Arguments’ which we define, not as a disagreement between two or more people, but as a reason, or set of reasons in support of an idea or conclusion. An argument in this context is the structure that links the evidence of an observation to a conclusion that explains some aspect of or system of the world we live in. Evaluating our own thoughts and beliefs is the backbone of science and our general understanding of the world because it provides a logical, reliable, and valid structure to figuring out what works and what doesn’t, to figuring out what is true and what isn’t, and it provides a method that alerts us when a conclusion is flawed. It is the method we use to establish how we fit into the world we inhabit, but more importantly, how we can use our resources (intellectual, material, and physical) to benefit us as a species.

Making a valid argument

Whether we are referring to a Deductive, Inductive, or a Probalistic argument these all share a similar structure in that they can be broken down into Premises and Conclusions. A Premise is a statement of fact. One example of a Premise is the fact that ‘Jupiter is bigger than the Earth’. We refer to this as being ‘True’ because it is 100% true, 100% of the time. This is important information for us to know when we decide if a conclusion is, or can be, correct. An argument may have more than one Premise, so in this case we could add, ‘the Earth is bigger than the Moon’. So again, this is true in that it is 100% true, 100% of the time as the Moons size or mass does not change, nor does the Earths. So, from these two Premises we can accurately conclude that ‘Jupiter is bigger than the Moon’. This conclusion is true because we know both of these Premises are 100% true, 100% of the time. This structure is a requirement of a Deductive argument. For this blog, I’ll focus on Deductive arguments as they’re the most prevalent and they’re the easiest to both apply and to detect errors, or invalid conclusions (in my opinion). Probalistic and Inductive arguments also have Premises but these differ in that for Probalistic arguments the Premise can be mostly true (either not 100% true, and/or not 100% of the time), and for Inductive arguments the conclusion doesn’t always have to be correct (either 100% or 100% of the time). So for now, let us focus on Deductive arguments.

There are two other requirements for a Deductive argument to be considered structurally valid. The first is that the Premise follow the Law of Transitive Properties and the second is that the conclusion must follow from the Premise. Let’s deal with the first: The Law of Transitive Properties (or Transitive Law) is that for the conclusion to be true (and the argument to be valid) the relative properties of one Premise must carry over to the relative properties of the other. For example, when we look at our earlier example:

Premise 1: Jupiter is bigger than the Earth.

Premise 2: Earth is bigger than the Moon.

Conclusion: Therefore, Jupiter is bigger than the Moon.

The relative property here is the size of the Planets in relation to each other. If, for example, we have an argument that does not follow this rule, we end up with a conclusion that is not reliable, therefore potentially invalid. An invalid argument that makes violates the law of transitive properties looks like:

Premise 1: The Earth is round

Premise 2: Basketballs are round

Conclusion: Therefore, the Earth is a Basketball

While it appears that the properties of one has been carried over to the other, what has been carried is a feature of the subject in the Premise, rather than the relative properties of the subjects to each other. Additionally, and this comes to the second additional requirement, that the conclusion must follow from the Premise. In the second example, the first and second Premise (the shape of the Earth and Basketballs) does not carry over to the conclusion, meaning the conclusion will not follow from the Premises.

We know that just because two objects share a similar feature does not mean they have any more in common than that single feature. This particular type of error, called Affirming the Consequent, is a type of Non-Sequitur Fallacy. Students of Science will be familiar with this in the form of ‘Correlation doesn’t equal causation’, but for the average person, committing this Fallacy means drawing a conclusion that two things are the same (or that one thing causes another) just because those two things share a common element, feature, or they just occur at the same time.

So in our Earth and Basketballs example, just because they’re both round, does not lead to a valid conclusion that Earth is a Basketball. While this may seem like a very obvious error, we often make this type of error in our daily lives. For example: If a professional sports person notices that on days when her team has won she happens to express a particular behaviour (for example on days there was traffic she is forced to take an alternate route to the game), she may conclude that these two events share more in common than mere chance. The sportsperson may conclude that this new route has had some mysterious impact on the likelihood of a win. In future, she may take this route to the game each time to increase the likelihood of a win or perhaps to avoid ‘Jinxing’ the game by avoiding to take the original route as she may have concluded that this was the occurrence that influenced the loss of the previous games. If this was the case, this person would be committing an ‘Affirming the Consequent’ fallacy. The alternative route, while correlating with a win, does not increase the likelihood of a win itself (nor does it decrease the likelihood of a win if the behaviour is discontinued), despite how it might make the player feel.

In fact, when we test the notion that two random events influence each other, we see that there is no correlation to the particular behaviour and the likelihood of a win. No matter how a person feels taking that particular route to a sporting event, it has no more than a chance effect on the outcome itself. One very well-known application of Affirming the consequent fallacy is the ‘Lie Detector Test’ or Polygraph as some may know it. Here we are asked to believe that if we tell a lie a machine we are connected to will sound an alarm and subsequently highlight our deception. This could be embarrassing in the least, and in the most, cost you your freedom. Think about a person who has committed a crime attempting to lie to the Police about their recent activity. In reality, the polygraph is merely one of many interview tools used by Police to ‘whittle down’ through deception to reveal truth. In this case, the more YOU believe this machine can tell you’re lying, the more effective the polygraph is and easier it is for the Police. In reality the use of this device and the subsequent belief that it can spot lies relies heavily on a Confirming the Consequent Fallacy. It goes a little like this. Premise 1: Changes in stress levels result in changes in physiological measurements. Premise 2: Lying results in changes in stress levels. Conclusion: Changes in physiological measurements are the result of increased stress levels caused by lying.

The issue here is twofold. Firstly, even though Premise 1 is completely true (100% true, 100% of the time; in-fact we use these types of measurement in Neuroscience and Psychology to both signify and measure changes in emotion in our research), Premise 2 is only true some of the time. However, even if we were to hold that Premise 2 was true 100% of the time, these Premises do not follow the law of transitive properties. Just because lying may result in changes in stress and changes in stress may result in changes in physiological measurements, does not mean this is the only cause of these changes. We (i.e. Psychologists) know that there are many things (uncontrolled for in these measurements and unmeasured) that may influence the stress levels of the person. Imagine how stressful it must be to be accused of a crime, or to suspect the Police implicate you in a crime that may rob you of your freedom. These influences include naturally anxiety, general nervousness, and fear. But can also include physical illness and medication. Affirming the consequent turns out to be quite prevalent in the day to day reasoning of people in general. Think of the last time you crossed your fingers (either literally or metaphorically) to influence a positive outcome. This is the Affirming the Consequent fallacy.

Probably the most commonly used fallacy is Ad Hominem. This is an attack on a person instead of the premise/conclusion of the argument. In committing this fallacy, the speakers’ argument is dismissed, not on the basis that their argument doesn’t have merit, or that their conclusion does not follow from the Premises, rather on the basis they are ‘not qualified’ to hold that opinion, or, don’t have the necessary experience. This type of fallacy comes in the form of a character assassination. Meaning that racial or religious slurs, insults based on a persons’ gender or education are used in place of addressing the content of the argument or conclusion itself. The goal here is to show that if the speaker themselves are shown to be unreliable or questionable, then by association so are their conclusions/opinion. It is a way to avoid addressing the content of an argument by attacking the speaker themselves. We see people do this most often when they are faced with information or an opinion that contradicts a favoured belief, opinion, or position. By attacking the speaker rather than addressing the content of the argument, the belief, opinion, or position goes unchallenged and subsequently sustained or protected. The inverse of Ad Hominem is Argument from authority. Here the person claims to have special knowledge due to their possessing some special education or experience that others do not possess. The purpose of this is the same as the purpose of Ad Hominem, to ensure that the favoured belief, opinion, or belief go unchallenged on their specific merits or validity.

These are but two of the many fallacies that we are both susceptible and subjected to in evaluating the information we are presented with on a daily basis. We are also susceptible to Bias, which, rather than being the result of an error in the structure of an argument, is a general inclination to interpret one, or many, situations from previous experience or opinion. This will be the topic of a future entry.