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What is logic? Strictly speaking it is the science or study of how to reason or evaluate arguments. Logic is not a matter of opinion; there are specific principles and criteria involved. What sounds reasonable may well be so, but this does not necessarily make it logical. In this article we look at some of the principles of logic, and how to apply them.
The Greek philosopher Aristotle is widely regarded as the father of logic, and indeed the word logic is thought to come from the Greek word ‘logos’, which translates variously as ‘rule’, ‘ratio’ ‘discourse’ or ‘reason’. Although others before him, including Plato, discussed the nature of arguments, and how to evaluate them, he was the first to develop systematic criteria for doing so.
Aristotle: the father of logic
All of Aristotle’s logic revolves around one notion, the deduction.
Aristotle says that ‘a deduction is speech in which, certain things having been supposed, something different from those supposed results of necessity of them being so’.
To put it another way, logic rests on the fact that there are statements that will always be true, and can’t be falsified no matter what is, or is not, the case. These statements are known as tautologies.
Some simple examples of a tautology include:
- It rains or it does not rain.
- No triangle is a circle.
- Everything is something.
It is impossible to find a situation where a tautology would not be true. Thinking about the examples above, there is no way to even imagine a situation where a triangle could actually be a circle. If a sentence were written stating this, it would be known as a contradiction. When it is said that something is illogical, then taken literally, the statement cannot possibly be true.
Logic, in one form or another is part of daily life. A modern day example can be seen in the plethora of puzzles such as Sudoku available in every newspaper. [1] According to John Duncan, of the Medical Research Councils’ Cognition and Brain Sciences Unit in Cambridge, the desire and ability to solve these puzzles originates in the frontal cortex, the same area of the brain we use when finding relationships between a series of different patterns, or predicting the next in a series. [2]
Logic and Causal Relationships
Galileo's observations of the planets led him to support the idea that the Earth revolved around the Sun.
A causal relationship occurs when one thing happens (the effect) as the direct result of another (the cause). For example, increased sales of a product following the employment of an additional member of the sales team are likely to be as a direct result of that employment. In order to establish a causal relationship, there are three logical criteria that must be met.
1. Timing
It must be possible to prove that the cause preceded the effect. In this case the increase in sales came after the recruitment of the additional person, so the timing is correct.
2. A correlation between cause and effect
In order for there to be a causal relationship, there must first be a regular relationship. There must also be an identifiable link in this relationship between cause and the effect. Again, the recruitment of the additional employee into the sales team forms an identifiable relationship with the increased sales.
3. Eliminate all other possibilities
There may be other plausible alternative explanations. These must first be eliminated. For instance, did the new employee join the team at the same time as a sustained advertising campaign, which could itself have generated the increased sales? All such possibilities must be explored and discounted before the relationship can be deemed purely causal.
When there is reasonable evidence of a causal relationship, that information can be used to intentionally alter the environment by producing, or preventing, the occurrence of certain types of event. Take, for example, two research teams at work. The teams are identical in every way including gender-split, working hours and aptitude for the role. The only difference is that Team A has had access to the internet for the past six months whilst Team B has not. Team A has recently consistently outperformed Team B in terms of the amount of output they generate. As the only difference between the two teams has already been identified, all that remains is to determine if this difference is causal or not.
- Timing
Team A has been outperforming Team B for five months now. This ties in with the introduction of the internet six months ago. - A correlation between cause and effect
It is possible to determine that Team A saves a significant amount of time by performing the majority of its research on the internet, whilst Team B has to spend time in the library. - Eliminate all other possibilities
By first generating a list of all possible reasons for the differences in output, each one can then be systematically eliminated. In this case, sickness, holidays, technical issues and motivation do not differ in any way from team to team.
It can, therefore, be said that there is a causal relationship between providing Team B with access to the internet and an increase in productivity.
Using Logic to Debate and Argue
Plato (left) wrote down the arguments of his mentor, Socrates, in the form of a dialog.
A debate is all about using argument and persuasion to convince others that an opinion is correct. One of the best ways to successfully debate a point is to approach it logically. Making a list of all the pros and cons for the point that is to be argued can help to ensure all points are considered, as can using the three criteria described above to establish a causal relationship
Another way of debating successfully is to consider the use of logical fallacies. These are errors in thinking, or mistakes in logic. There are many logical fallacies, and here are some of the more common ones:
- Post hoc fallacy
This is the assumption that because one thing happens before the other it is the cause of the other. A classic example is that of the rooster who believes it is his crowing which causes the sun to rise in the morning, and is shamed when after remaining quiet for a day it is proven that the sun will rise anyway. - False authority
An expert is someone who has broad knowledge and experience of a subject area due to study and credentialed expertise, as opposed to someone who has a limited amount of hands-on experience. For instance, a thief is not an expert in criminology. - Part/whole
Proving that part of an argument is right or wrong does not necessarily prove or disprove the whole argument. Proving that someone can run 100 meters in 10 seconds does not prove someone can run 1000 meters in 100 seconds. - Either/or
It should not be assumed that because one thing is true, then another is false. There may well be other options. For instance, the man who works 70 hours a week and says he is too tired to enjoy life, states his only two options are either to be tired or unable to pay the bills. However, he could seek a better paid job or look for ways to cut his outgoings. - Red herrings
Originally, a strong-smelling fish was dragged across a trail of scent to throw off blood hounds. Now the term is more commonly used to represent the introduction of a distraction into a debate and to disrupt its course.
These logical fallacies are useful in a number of ways. They can be used when preparing for a debate, to help the debater consider all the angles the opposition may cover, as well as being used strategically to introduce confusion. Being aware of logical fallacies can also help the debater ensure that the logic they plan to use during an argument is not flawed by inadvertent use of a fallacy.
Conclusion
Logic is a vast and complicated area. At its simplest and best it can help determine the cause of a problem, assist with decision-making, and aid the construction of a well thought out argument. At its most complicated it can be a vast and obscure subject for serious philosophers. The truth of the matter, though, is that wherever there is a reason or an argument there is an underlying use of logic, and without applying that logic we cannot assume our reasoning is sound.
References[1] A logic based number puzzle.
