If Philosophy

Argumentation: From Premises to Conclusions

What is an argument? Oftentimes people speak of arguments as reasons to believe a particular statement. That usually works well, but we will try to be a bit more technical in our analysis. That way we can name different things differently, and hopefully speak of them a little more clearly.

Arguments, the way we are to understand them, are comprised of two types of entities, namely premises and conclusions. Premises are propositions that serve the role of trying to justify another proposition that, in the best of circumstances, follow logically from themselves. Themselves? The premises! In turn, we call the thing that premises are to justify for the conclusion. An example of an argument that consists of two premises and one conclusion follows.

P1) All cats are cute
P2) Felix is a cat

Therefore,

C) Felix is cute.

All three of these steps, as I just said, make up an example of an argument. P1 and P2 constitute the premises that serve to justify the conclusion, C, namely that Felix is cute. This argument is, moreover, what we classify as a deductively valid argument. Why? Well, briefly put, the argument is such that the conclusion must be true if (and I stress, if!) the premises are true in virtue of its form. An argument’s form, in brief, is given by the relations that hold between the premises and conclusions. If it is the case that all cats are cute and that the critter I’m pointing to right now, Felix, is a cat, then it would follow that Felix is cute. He’s a cat after all, and as P1 says, all cats are cute.

Now, even if it turned out that all cats weren’t cute, this argument is nevertheless deductively valid. Moreover, even if Felix isn’t a cat, the argument is still deductive. But why? “You just said that the premises are true in deductively valid arguments, didn’t you?” Well… Not quite.

The important thing to grasp here is the hypothetical nature of the definition. It states that if it happens to be the case that the premises are true then the world must be in such a way that the conclusion is true, too. When we are to determine whether an argument is deductive or not, it does not matter, strictly speaking, whether or not the premises in fact are true. We are only interested in what would have to be the case if they happen to be true. Try as hard as you can to imagine a world where it is the case that all cats are cute, where Felix happens to be a cat, yet Felix isn’t cute. You can’t.

Deductively valid arguments, to reiterate, are such that their conclusions must be true, if their premises are true. There are deductively valid arguments of many kinds, and some of them even have names. That one above about Felix is called a syllogism. Why? Aristotle said so, or something close to it at least. Other examples such as modus ponens and modus tollens exist. The names are not too important right now, but suffice it to say that while there are many deductively valid arguments that have been named, an infinite amount of others have not; despite all the time humans have spent studying the subject.

Phew! Surely, that’s got to be everything to it, right? Yeah, not quite. Again.

We now know roughly what a deductively valid argument is. But what’s the point of that? The point is that we can now distinguish these from another kind of argument. I’ll first give you the name of them, and hopefully explain what they are in short order. They’re called inductive arguments.

So, what are they? It might be easier to understand what they are by contrasting them with deductively valid arguments which we already have a grasp of. Whereas deductively valid arguments must have true conclusions when their premises are true, inductive arguments do not have to have true conclusions even if their premises are true. But why would we want to ever use such arguments? Surely we want our reasons for accepting a proposition to be conclusive! Yes, sure. Often that is the case. But sometimes we simply can’t reach such levels of confidence. I’ll illustrate why with an example of an inductive argument.

P1) Most people with English-speaking parents speak English fluently.
P2) Kim is a person with English-speaking parents.

Therefore,

C) Kim speaks English fluently.

Alright, so far so good. What’s different about this argument? Most importantly, for our current purposes, it’s the quantifier “most” having replaced the quantifier “all” from the first example argument. This allows room for Kim to be part of the group that speaks English fluently, but it also leaves some room for Kim to be part of the group that for whatever reason does not speak English fluently. How could this be so? One reason might be that Kim is only six months old. Expecting her to speak English fluently – or any language for that matter – is a bit much to ask at that age.

Inductive arguments, then, can have all of their premises being true, but still not have their conclusions’ truth guaranteed. It might well be the case that most people with English-speaking parents also speak English fluently. It might also well be the case that Kim is such a person. But, as we saw, that is not a guarantee of her aptitude in speaking English. If the undermining proposition that she is six months old is true, we might do best to treat the conclusion as false.

We use inductive arguments in areas of arguments where there are some uncertainties or probabilities less than 1 but greater than 0. That’s quite often. Not always, but often enough. They have their use, just like deductively valid arguments. Their areas of application differ, however, and it serves us well to be mindful about what kinds of arguments we supply for the conclusions we intend to reach. Moreover, it serves others well if we represent their points of view with as credible arguments as possible when we are to evaluate them. Sometimes that is by using deductive (or “valid”) arguments, at other times it is by categorising their points through inductive arguments.

Summary

We have reached the point where we can say that arguments consist of premises and conclusions. Premises are propositions that serve to justify some other statement. This other statement we call the conclusion. Deductively valid arguments are such that their conclusions must be true given that their premises are true. This is what we can call a ‘formal property’. The deductively valid arguments have true conclusions when their premises are true because of the way the premises and conclusions are related. Inductive arguments, by contrast, can have false conclusions even when their premises are all true. We can and may use both kinds of argument, but for somewhat different purposes. It’s therefore probably a good idea to be mindful of your own intentions, and those of others, when arguing.

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