Being able to argue properly, with yourself and others, is an incredibly valuable skill. Being able to critically evaluate arguments is not only extremely useful in the workplace – it can help you make better life choices for yourself and the people around you. This skill is generally known as “critical thinking”, and it is a philosopher’s bread and butter. Now, there’s no point in denying that we all use our brains differently, and that some of us are naturally good at this kind of thinking. But anyone can get better at thinking critically by studying arguments, including those to whom it comes naturally. So, for your entertainment and edification, I’ve decided to put together a few posts on the topic.
Let’s start with deduction. A deductive argument, simply speaking, is one in which the premises (if true) guarantee the conclusion. In other words, if the premises of a valid deductive argument are true, the conclusion can’t possibly be false. An example of this could be; “If I don’t study for my philosophy exam on wednesday, I will not get a good mark on it (first premise). I’m not studying for my philosophy exam on wednesday (second premise), therefore I will not get a good mark on it (conclusion)”. As you can see, if the premises of this argument are true, the conclusion must also be true. Note that this doesn’t mean that the conclusion actually is true, because the premises might be false. Compare this to; “If I don’t study for my philosophy exam on wednesday, I will not get a good mark on it. I will study for my philosophy exam on wednesday, therefore I will get a good mark on it”. This is a bad argument, deductively speaking, because the premises don’t guarantee the conclusion. This is because the form of the argument is invalid. I’ll get to validity later, but for now I want to focus on conditionals.
Conditional statements (often shortened to “conditionals”) are statements like the first premise in the example arguments above. “If then” statements, essentially. Conditional statements contain two different conditions (hence the name): a necessary condition and a sufficient condition. To put it very simply, the sufficient condition is the one that comes after the “if”, and the necessary condition is the one that comes after the “then”. In the examples above, “not studying for my philosophy exam” is the sufficient condition and “not getting a good mark on it” is the necessary condition. The “if” and “then” are not part of the conditions. Knowing the difference between these different kinds of condition, and being able to identify them, is an essential skill when it comes to evaluating deductive arguments.
However, identifying them can be difficult, because conditional statements are often not given in the standard “if then” form. In such sentences, it’s possible to work out which is which by looking at the meaning of the statement (what is necessary and what is sufficient), but it’s also possible to translate it into “if then” form. Consider this statement: “only people who don’t study for their philosophy exam will get a bad mark on it.” This translates into: “if you get a bad mark on your philosophy exam, then you didn’t study for it.” The original sentence does not say that everyone who doesn’t study for their philosophy exam will get a bad mark on it; rather, it says that those who do get a bad mark will not have studied. This becomes a lot clearer when the sentence has been translated, because it’s easier to identify the conditionals.
There are various different ways in which you can go about translating conditional statements, such as memorizing certain key words and phrases (“only if”, for instance, usually precedes a necessary condition), but I’ve found that the easiest way is to use a conditional statement that you know is true (preferably one that’s very obviously true), and seeing how it would be rearranged in the form of the sentence you’re translating. I tend to use “if you’re a father, then you’re a parent”, which was the example given to me when I was learning how to do this. Consider the example sentence I gave you earlier. If I translate my “if then” sentence into the form it has, I get “only parents are fathers” (since the “if then” sentence is true, it must still be true when it’s rearranged – that’s how I know where to put the “father” and where to put the “parent” – “only fathers are parents” would be a false statement). I can now see that the necessary condition and sufficient condition have changed place, with the necessary condition coming first. All I have to do now is identify what the original conditions were (“not studying for your philosophy exam” and “getting a bad mark on it”) and lable them as necessary and sufficient.
Translating conditional statements like this is a skill, and as such you have to practice doing it. There’s a great little game on Khan Academy that let’s you do just this (don’t worry, it’s not too mathsy): https://www.khanacademy.org/math/geometry/logical-reasoning/e/conditional_statements_2
You can also find more information on conditional statements and deductive arguments on that page – I’ll be following up on this post with one on deductive validity in the near future. Until then, I hope you are well, and as always if you have any questions or suggestions please leave a comment below!