from the premises necessarily (see 1.2). Calling a deductive argument ‘valid’ affirms that the conclusion actually does follow from the premises in that way. Arguments that are presented as or taken to be successful deductive arguments, but where the conclusion does not in fact definitely follow from the premises, are called ‘invalid’ deductive arguments.
The tricky thing, in any case, is that an argument may possess the property of validity even if its premises or its conclusion are not in fact true. Validity, as it turns out, is essentially a property of an argument’s structure or form; and so, the content and truth value of the statements composing the argument are irrelevant. Let’s unpack this.
Consider structure first. The argument featuring cats and cheese given above is an instance of a more general argumentative structure, of the form:
1 All Xs are Ys.
2 Z is an X.
3 Therefore, Z is a Y.
In our example, ‘block of cheese’ is substituted for X, ‘things that are more intelligent than all philosophy students’ for Y, and ‘Meg’ for Z. That makes our example just one particular instance of the more general argumentative form expressed with the variables X, Y, and Z.
What you should notice is that you don’t need to attach any particular meaning to the variables for this particular form to be a valid one. No matter with what we replace the variables, it will always be the case that if the premises are true (even though in fact they might not be), the conclusion must also be true. If there’s any conceivable way possible for the premises of an argument to be true but its conclusion simultaneously be false, any coherent way at all, then it’s an invalid argument.
This boils down to the notion of validity as content‐blind or topic‐neutral. It really doesn’t matter what the content of the propositions in the argument is – validity is determined by the argument having a solid, deductive structure. Our block‐of‐cheese example is then a valid argument, because if its ridiculous premises were true, the ridiculous conclusion would also have to be true. The fact that the premises are ridiculous is neither here nor there when it comes to assessing the argument’s validity.
The truth machine
Another way of understanding how arguments work as to think of them along the model of sausage machines. You put ingredients (premises) in, and then you get something (conclusions) out. Deductive arguments may be thought of as the best kind of sausage machine because they guarantee their output in the sense that when you put in entirely good ingredients (all true premises), you get out a fine‐quality product (true conclusions). Of course, if you don’t start with good ingredients, deductive arguments don’t guarantee a good end product.
Invalid arguments are not generally desirable machines to employ. They provide no guarantee whatsoever for the quality of the end product. You might put in good ingredients (true premises) and sometimes get a high‐quality result (a true conclusion). Other times good ingredients might yield a frustratingly poor result (a false conclusion).
Stranger still (and very different from sausage machines), with invalid deductive arguments you might sometimes put in poor ingredients (one or more false premises) but actually end up with a good result (a true conclusion). Of course, in other cases with invalid machines you put in poor ingredients and end up with rubbish. The thing about invalid machines is that you don’t know what you’ll get out. With valid machines, when you put in good ingredients (though only when you put in good ingredients), you have assurance. In sum:
Invalid argument
Put in false premise(s) → get out either a true or false conclusion
Put in true premise(s) → get out either a true or false conclusion
Valid argument
Put in false premise(s) → get out either a true or false conclusion
Put in true premise(s) → get out always and only a true conclusion
Soundness
To say an argument is valid, then, is not to say that its conclusion must be accepted as true. The conclusion is definitely established as true only if both of two conditions are met: (1) the argument is valid and (2) the premises are true. This combination of valid argument plus true premises (and therefore a true conclusion) is called approvingly a sound argument. Calling it sound is the highest endorsement one can give an argument. If you accept an argument as sound, you are really saying that one must accept its conclusion. The idea of soundness can even itself be formulated as an especially instructive valid, deductive argument:
1 If the premises of the argument are true, then the conclusion must also be true (i.e. the argument is valid).
2 The premises of the argument are true.
3 Therefore, the conclusion of the argument must also be true.
For a deductive argument to pass muster, it must be valid. But being valid is by itself not sufficient to make it a sound argument. A sound argument must not only be valid; it must have true premises, as well. It is, strictly speaking, only sound arguments whose conclusions we must accept.
Importance of validity
This may lead you to wonder why, then, the concept of validity has any importance. After all, valid arguments can be absurd in their content and false in their conclusions – as in our cheese and cats example. Surely it is soundness that matters?
Okay, but keep in mind that validity is a required component of soundness, so there can be no sound arguments without valid ones. Working out whether or not the claims you make in your premises are true, while important, is also not enough to ensure that you draw true conclusions. People make this mistake all the time. They forget that one can begin with a set of entirely true beliefs but reason so poorly as to end up with entirely false conclusions. It can be crucial to remember that starting with truth doesn’t guarantee ending up with it.
Furthermore, for the sake of launching criticisms, it is important to grasp that understanding validity gives you an additional tool for evaluating another’s position. In criticising a specimen of reasoning, you can either:
1 attack the truth of the premises from which he or she reasons,
2 or show that his or her argument is invalid, regardless of whether or not the premises deployed are true.
Validity is, simply put, a crucial ingredient in arguing, criticising, and thinking well, even if not the only ingredient. It’s an utterly indispensable philosophical tool. Master it.
SEE ALSO
1 1.1 Arguments, premises, and conclusions
2 1.2 Deduction
3 1.5 Invalidity
READING
Aristotle
