When standardisation was first introduced, we saw that it is sometimes necessary to make explicit a premise which was not fully stated in the argument.
(2a) Only outstanding musicians are accepted into the orchestra. So given what we know about Wally's musical talents, he is not going to get in.
Would be standardised as:
1 Only outstanding musicians are accepted into the orchestra 2 Wally is not an outstanding musician
C Wally is not going to get into the orchestra.
The second premise has been put into a clear propositional form, and we can see from this standardisation that the argument is a valid conditional argument.
In many longer arguments, the conclusion will not be stated at all, and in those cases it is necessary to decide what point the author of the argument is trying to convince the audience to believe, and use that as the main conclusion in your standardisation. This is something you have had practice of in giving argument summaries, and broad standardisations.
Whenever it has been necessary to make a premise or conclusion explicit, we apply the principle of charity, by choosing a statement of the proposition which is no stronger than it needs to be (hence we state premise 2 in the argument above as "Wally is not an outstanding musician", which is all that is needed for the
argument, rather than "Wally is an abysmal musician", which might be more than was intended.)
The point of finding missing premises or conclusions like this was just to make the argument clearer, by putting all the parts of the argument into clear propositional form. In this sense, clarifying missing premises or conclusions is just a matter of explicitly and clearly formulating all parts of the argument .
There is, however, another sense in which an argument may contain a missing premise, which may not be so innocuous.
In many cases an argument will involve suppressed premises: it will be making assumptions which are necessary for the inference to be acceptable, but which are not stated, and are therefore not given any justification. Sometimes the assumptions which are made will just involve commonly accepted background information, but in other cases, assumptions may be made which are far more controversial. If controversial premises have just been assumed without justification, this will be a weakness in the argument.
The fact that an argument involves suppressed assumptions may or may not be a problem. It is not a problem if it is only generally accepted beliefs which are assumed. It is a problem if the assumptions are controversial.
To clarify this distinction, consider the following arguments, each of which seem to rely on the assumption of information which is not explicitly stated:
(2b) That car is hardly big enough to fit twelve clowns in it, so there is no way they could fit twenty.
(2c) Fido is a dog, so he couldn't live underwater.
(3d) Abortion is wrong, because killing a human being is always wrong.
In each of these arguments, we need to bring some extra information to the argument to understand why the conclusion is supposed to follow from the premise. In the first argument, the assumptions which might be being made are all uncontroversial: "twenty is more than twelve" perhaps, or "If you can hardly fit twelve of something somewhere, you can't fit twenty". These are propositions which anyone would accept, so you would not need to make a point of this if you were evaluating the argument.
The second case involves an assumption that dogs can't live underwater. Again, this relies on some background knowledge, but it is something that anyone would accept as common knowledge, so the fact that the argument does not make this explicit would not be a reason to object to the argument. Provided that the intended audience was composed of people we could expect to share our basic background beliefs, these inferences would be acceptable.
The third case, however, is different. The argument as it stands is:
(2d-i) 1 Killing a human being is always wrong C Abortion is wrong
Does the conclusion follow from the premise?
It follows only if we accept the controversial assumption that abortion involves killing a human being, ie that a foetus is a human being. The intended argument seems to be something like this:
(2d-ii) 1 Killing a human being is always wrong
[2 Abortion involves killing a human being] Suppressed premise C Abortion is wrong
This new premise, 2, is not something which can just be assumed as background knowledge, because this is really one of the important points of dispute in the abortion debate.
When an argument relies on a controversial assumption, this is something which should be noted in your evaluation, because it constitutes a flaw in the argument. If a premise is controversial, as we have seen, it should be supported by some evidence. It is not permissible to furtively sneak premises into your argument if they are premises with which an opponent might disagree.
To work out if there are any suppressed premises/assumptions which need to be noted in your evaluation of an argument, look at any inferences which seem incomplete, and ask yourself
"What would the author have to have been assuming, to think that the conclusion followed from these premises?
If there are assumptions which are just common knowledge, then this is not a problem, but if you find something which is being assumed, but which would require further justification, this is something to which an objection should be raised.
Examples
Each of these arguments involve some kind of suppressed premise. In which case is a questionable
assumption made, and in which cases is it acceptable, relying only on what could reasonably be considered background knowledge?
(1) We should not allow boat people to into this country, because we do not want terrorists based here.
This argument is based on the suppressed premise that boat people are likely to be terrorists. This is not a premise which could be accepted without being supported by evidence.
(2) On average, women get paid less than men. This shows that despite sex discrimination laws, men still get paid more for the same work.
This argument relies on the assumption that women and men do the same work. This is probably not true, because more women than men stay home with children or work part-time, thereby bring down the average income, and the sexes are not evenly represented in different professions. Therefore the fact that on average women do not get paid as much as men does not establish that they get paid less for the same work.
(3) You can't keep a cat in your unit, because it's a condition of your lease that you don't keep any pets.
This involves a suppressed premise that a cat which you keep in your unit would be a pet. This seems acceptable as common background knowledge.
(4) Brad votes Labor. So Brad is probably a communist.
This rests on the assumption that people who vote Labor are likely to be communists. This is not an acceptable assumption.
(5) Debbie has two children. So Debbie is a mother.
This conclusion follows from the premise if we assume that "Debbie" is likely to be a woman's name, rather than a man's. While we cannot be certain of this, it would be acceptable to assume this as a commonly shared belief, at least in our society.
(6) Britney was miming at her concert. She must not actually be able to sing.
The assumption here is that if Britney could sing, she would have done so. This may not be justified, because there may have been other reasons that Britney mimed at her concert.
(7) Abortion is perfectly legal, so obviously there's nothing wrong with it
This argument rests on the assumption that if something is legal, then there is nothing wrong with it. This would not be acceptable in the context of an argument over the acceptability of abortion, because the point of dispute would not be about whether abortion was legally permissible, but about whether it was morally permissible.
The question you should be asking yourself in evaluating any inference is: Do these premises really provide good evidence for the conclusion? Do they give me good reason to accept the conclusion? Arguments (1), (2), (4), (6) and (7) above are examples of arguments which are flawed, because they require us to assume things that we shouldn't simply assume. By thinking about what the assumption is (rather than just saying the inference is no good), we get a better idea of what is going wrong in the argument, and what kind of evidence would be required to fix it.