If Philosophy

Argumentation: Analysis and Evaluation

So far we’ve gathered that there are deductive and inductive arguments. They consist of premises and conclusions. So what? Well, analysing arguments in part involves deciding what form they have, and so if they are deductive or inductive. Once this is done, we can begin to evaluate them.

How do we evaluate them and so check their credibility, though? We don’t do it by simply looking at the conclusions and asking ourselves whether we’re inclined to agree with them or not. Instead we look to, and at, the premises. Why? Recall from Argumentation: From Premises to Conclusions that premises are propositions that are intended to justify conclusions. We’re therefore interested in whether they succeed or not. Even if the conclusion reached in some argument doesn’t sit well with us, the premises might provide ample reason for us to accept it. Insofar as we are rational that is, and being rational seems like the sort of thing we want to be.

Let’s look at an example argument to see what this entails. Consider the following:

P1) If Queen Elizabeth is in Buckingham Palace, then Queen Elizabeth is in London.

P2) Queen Elizabeth is in Buckingham Palace.


C) Queen Elizabeth is in London.

So, we’ve got an argument analysed into its component parts. Now we turn to evaluating it.

Evaluating Premises’ Tenability

At this point we have two tasks in front of us. We can (1) consider whether or not P1 and P2 are reasonable to believe, and we can (2) consider whether or not them being reasonable to believe provides us with good reason to accept the conclusion C; that Queen Elizabeth indeed is in London. Let’s begin with task number one. I may not know much about the British monarchy, but one thing I do know is that Buckingham Palace is situated in London. I once saw it on a trip by mistake. (Long story. Well, not really, it was a weekend trip.) Anyway, being in Buckingham Palace is sufficient for being in London, so P1 seems reasonable to accept. If someone is in that old building, then they’re in the capital city of England. Huzzah! Can we accept the argument now and move on? Not just yet.

What about the second premise (P2)? Now, it might seem reasonable to believe that Queen Elizabeth is in her palace, but just like Princess Peach in those old Super Mario games happened to be in another castle (time and time again…), so might the Queen of England be. In fact, she might be just about anywhere else. Right now I don’t find myself with very good reason to believe that she’s in Buckingham Palace. It’s approximately five p.m. as of writing this. Perhaps she’s gone to the pub two towns over for an after work get-together? Maybe not, but perhaps she’s off somewhere on official business. That seems like the sort of thing she would be up to. Therefore, I may not have sufficient reason to believe that she is in London. Note, however, that I didn’t start by assuming that she isn’t in London, but arrived there by way of evaluating the premises P1 and P2. So far so good. P1 and P2 have both been dealt with in terms of their tenability. Now we’re done, surely? Nope!

Evaluating Premises’ Relevance

Well, why aren’t we done? I’ve accepted P1 but rejected P2. That’s my purported reason for declining to accept the conclusion, C. If I had accepted both P1 and P2 then I would have been rationally forced to accept C. And as I said, rationality seems like the sort of thing we want to promote. If you don’t, I wish you luck dodging the barrage of ad hominems that you’ve probably got coming.

The point is this. Relevance is the degree to which a series of premises’ strengthen (or ‘support’) a conclusion under the assumption that the premises are true. The highest form of relevance is obtained by deductive arguments, since for these arguments, it is the case that if the premises are true then the conclusion must be true, too. The argument we’ve been discussing so far has been deductive, and I therefore deem the relevance to be as great as it can be.

This concept of relevance can, as might be expected, be applied to inductive arguments as well. Relevance is a matter of degree. Inductive arguments may well strengthen their conclusions by way of their premises, but since these can have false conclusions even when their premises are true, their premises’ relevance is never wholly complete. But in this instance, I do deem the premises to be oh-so relevant.

Sufficient and Necessary Conditions

Now, let’s get a little bit technical. I said that being in Buckingham Palace is sufficient for being in London. What’s that all about, anyway? Something, S, being a sufficient condition for E, is such that if S obtains, that is “enough” for E to also obtain. Whatever S and E may be short for, if S is sufficient for E, and S obtains, then we may be sure that E obtains as well. Okay, so what about E here? Do we have a fancy term for this term, too? Sure we do.

E is what we call a necessary condition for S. Why? Well, let’s think about this a little bit. We just said that if S obtains, then E obtains. But that means that we cannot have S be the case without E also being the case. That’s what it means for E to be a necessary condition of S. Think of it this way. If the Queen of England is in Buckingham Palace, then she must be in London. But that means that it’s necessary that she is in London if she is in Buckingham Palace. Of course, the Queen of England may be somewhere other than Buckingham Palace even though she is in London. Perhaps she’s visiting the parliament, or any number of other things that she could do in London. And that is precisely an example of the difference between sufficient and necessary conditions. Sufficient conditions bring about their correlate without fail, necessary conditions only allow for their sufficient correlates to obtain.

Okay, so much for that interlude. Let’s get back to whatever it was we were doing. Evaluating premises, was it? Sure. That. Take P1 for example:

P1) If Queen Elizabeth is in Buckingham Palace, then Queen Elizabeth is in London.

We might do well to evaluate this premise as true, given that being in Buckingham Palace is sufficient for being in London. Someone who did not know this, however, might respond that there’s no more reason to believe P1 than there is for her to believe that the number of grains of sand in the Sahara is even.

The proposition does not alter its truth-value regardless of this. The proposition is either true or false, but not both true and false at the same time. We therefore need to distinguish between taking something to be true (or false) and its being true (or false). When a deductive argument (those whose conclusions have to be true if their premises are true) has true premises, we call it sound.[1] Deductive, that is to say; valid, arguments can thus be either sound or unsound. A deductive argument is unsound if and only if at least one of its premises is false.

The same goes for considering premises to be false, and them actually being false. An argument may well be sound without my acknowledging that it is. Since omniscience isn’t one of the features us human beings come with, this gap is something we have to come to terms with. Whilst the gap cannot be removed entirely, we can do our best to make sure it is as small a gap as possible.


So, in the end, where are we at? We’ve said that once an argument is reconstructed, we can evaluate it. We do this by (1) looking to the credibility of the argument’s premises, and (2) checking their relevance for the proposed conclusion. In order to facilitate this work, an understanding of necessary and sufficient conditions helps. Necessary conditions of something must obtain if that something obtains. Sufficient conditions for something to obtain are such that if they obtain, that very something they were sufficient for obtains as well. We’ve also come to the conclusion that there’s a difference between taking something to be true (or false) and its being true (or false). We may not always evaluate arguments correctly, but we should probably do so fairly. The above might help in this endeavour. Or it might not. That’s for you to evaluate.

[1] This is not to be confused with that old question of whether a tree falling in the forest with no one around to here it makes a sound. We won’t be dealing with that question here and now.

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