We use arguments on a daily, even hourly, basis. Children argue with their parents all the time; bosses argue with their employees, and wives with their husbands! With due apologies to any children, bosses, and wives here (just kidding though)! Coming back to business, what is it that decides whether an argument is valid? Let’s take a look.
In logic as a discipline, arguments have a definite structure. They begin with a premise or two, or more, and then the reasoning flows until a conclusion is reached. So there are three basic parts of an argument: Premise(s), Reasoning, Conclusion.
But what’s a premise?
A premise is a basic assumption taken as a given fact upon which the reasoning is built to drive a conclusion across. Sample this:
(1a) All spheres are round.
(1b) The Earth is a sphere.
(1c) Therefore, the Earth is round.
In this argument, points (1a) and (1b) are the premises, and (1c) is the conclusion.
If the conclusion naturally or necessarily follows from the premises then the argument is said to be ‘valid’, as in the above case. Conclusion following naturally from the premises means there are no flaws in the reasoning. Whereas, if there are flaws (or ‘fallacies’ in philosophical terminology), then the argument doesn’t naturally follow from the premises and the argument is called out to be ‘invalid’. You might find it beneficial to know the common fallacies that people often commit while making arguments; I’ve thus put some useful links on logical fallacies at the end of the article, do go through them once at least, you’ll be really surprised to know how commonly we commit those fallacies in our daily reasonings!
Now, the premises can as well be challenged and proven to be false. In case the premises are proven to be false, then the argument is not ‘sound’ although it could be ‘valid’. Sample this:
(2a) All spheres are three sided.
(2b) The Earth is a sphere.
(2c) Therefore, the Earth is three sided.
This is a ‘valid’ argument as the conclusion follows necessarily from the premises; but it’s not ‘sound’ due to its first premise being false since spheres don’t have three sides! Thus, you can make an argument which is valid but not sound! And if your argument is valid in addition to your premises being true, that is when your argument is ‘sound’ as in the sample argument 1a-1c. Remember this: All sound arguments are valid, but all valid arguments are not necessarily sound.
So now you know the difference between a valid and a sound argument and hence you must have figured out why the sub-heading of this article says ‘Rationality doesn’t guarantee Truth!’ That’s because rationality entails valid reasoning to arrive at conclusions, but mere validity is not enough for the conclusions to be true, soundness is also a requisite for the truth to be arrived at (as in 1a-1c), otherwise you could reach a valid yet false conclusion (as in 2a-2c). Keep this cardinal principle in mind as it would be applied frequently in our analyses of the existence of God, Truth of Islam and related issues.
You must have also understood that making a ‘sound’ argument isn’t easy since it’s a really tough task to vouch for the truth of the premises! Sample this:
(3a) God is Merciful.
(3b) Humans have been created by God in the image of God.
(3c) Therefore, humans are merciful.
This is a valid hence rational argument but its soundness hence its truth can be disputed since premises 3a and 3b can be challenged by philosophers, scientists, and social scientists! So what determines the truth of the premises? How do we assure that the premises of an argument are true? You can read my article on the matrix of epistemology to get a brief and crisp insight into this issue which according to me is the most fundamental basis of all knowledge! But before you do so, let’s go a step further in our discussion on logical arguments, to know that there are two types of arguments: Deductive and Inductive.
Deductive versus Inductive arguments
All sample arguments presented so far are deductive in nature. A deductive argument is one whose conclusion always necessarily follows from the premises, i.e.; a deductive argument is always valid. Inductive arguments on the other hand may or may not be valid as they involve generalizations which may turn out to be false upon inspection. Sample this:
(4a) All the hundred men in a given region are observed to be white.
(4b) Therefore, the 101st man to be observed would also be white.
This is an inductive reasoning. It’s easy to see why this might be false, as there’s a chance that the 101st man might turn out to be brown or black!
Take another example:
(5a) All electrons observed so far have been found to carry a negative charge denoted by e = 1.6 x 10-19 coulomb. (Don’t fret about the complicated looking number here, just consider the symbol ‘e’ and focus on the message, not the numerical details!)
(5b) Therefore, all electrons in the universe carry a negative charge of e = 1.6 x 10-19 coulomb.
This conclusion is inductive, and it might stand rejected even if one electron is ever observed carrying a charge of a different value in any part of this universe!
Inductive reasoning is employed all the time, especially in science. The truth of inductive conclusions are probabilistic, not certain. Thus science too leads to probabilistically true results, not necessarily True results! We’ll discuss this in more detail in another article wherein I’ll discuss the scientific method and its limitations at length!
Reaching true conclusions through invalid or unsound arguments
Let’s add a twist to the story now! Sometimes, you could reach a true conclusion despite making an unsound or an invalid argument. Surprised? Sample this:
(6a) All successful people are smart and hardworking.
(6b) Elon Musk is successful.
(6c) Therefore, Elon Musk is smart and hardworking.
The above argument is valid but not sound. It’s not sound because its first premise is false, since there exist successful people who are not smart or who are lazy. Despite the argument being unsound, the conclusion is true, as we know from concurrent reports that Elon is indeed a hard working genius! Thus, sometimes, facts derived as conclusions of unsound or invalid arguments too turn out to be true on the basis of independent corroborative observations reported concurrently! So, just as you might reach a false conclusion despite being rational, you could as well reach a true conclusion despite being invalid or unsound in your argumentation! But if the scenario is so muddled up, then how can we be certain about the truth of a conclusion? Let’s look at the matrix below to clarify this.
| Type of argument | Status of argument | Conclusion |
| Induction | – | May be true or false |
| Failed deduction | Invalid | May be true or false |
| Deduction | Valid and unsound | May be true or false |
| Deduction | Valid and soundness undecided | May be true or false |
| Deduction | Sound | Definitely true |
Thus the only definite way of obtaining absolutely certain truth is through sound deduction! Every other way is uncertain in terms of its result and needs corroboration from independent sources. Yet, despite having established that only sound deduction fetches definite truth, the fundamental question remains: How do we establish the truth of the premises of a sound deductive argument? Ripe time to visit the matrix of epistemology now! Keep reading folks.
Some useful links on logical fallacies:
Fallacies (Stanford Encyclopedia of Philosophy)