For the first part of the textbook and course, most of our examples – both arguments in prose and arguments in maps – will be fully stated. This means that they will have all the necessary premises, and will be spelled out fully and explicitly, with nothing missing or left implicit.
But, as a few seconds of thought will show, most real life arguments are not fully spelled out (thank goodness!); they have unstated premises, unstated conclusions, and so on. They are like this: “Mary has a bad cold so she won’t be going to the party.” People don’t say things like: “Mary has a bad cold and people with bad colds don’t go to parties, so Mary won’t be going to the party.“
Since fully stating every argument can get tedious, and since real people rarely do it anyway, why in the world does this course start with fully stated arguments?
It will be useful to start by stating everything explicitly, so you get used to thinking in terms of the structure of an argument as a whole, with all its necessary elements. Then when you start making arguments more realistic, and leaving parts implicit, it will be clear what is being left out.
Reasons and objections are the most important elements in arguments. They are the primary level at which we reason. The English word reason is used in several different ways. However we are mostly interested in just one of them:
A reason is a set of one or more claims that jointly provide grounds for accepting a claim.
That is, a reason supports a claim, increasing the probability that it is true. Strong reasons considerably increase the probability that the claim is true; weak reasons only slightly increase the probability. The claim that a reason is put forward to support is a conclusion. The simplest argument is one consisting of a single reason supporting a conclusion:
Here the two claims 1A-a “Regular exercise is good for you” and 1A-b “You should do what is good for you” are put forward as evidence that the claim “You should get some exercise” is true.
Often a conclusion will be supported by more than one reason; we can add a second reason 1B to reason 1A to create this larger argument:
There is no limit to the number of reasons that may support a conclusion:
The reasons are independent of one another, in the sense that if one of the reasons is rejected, the other reason will support the conclusion as much as it did before.
Also, there is no limit to the number of reasons you can have in a line or chain of reasoning – reasons may be supported by reasons which are themselves supported by further reasons and so on and so on:
What is providing grounds for accepting another claim? The basic idea is that, if the proposed reason is any good at all, the premises increase the probability that the conclusion is true. People talk about this relationship in many ways, depending on the strength of the reason:
An objection is a reason against a claim. While a reason for a claim provides considerations/evidence in favor of the claim, an objection does the opposite – it provides considerations/evidence against the claim.
An objection is a set of one or more claims that jointly provide grounds for not accepting a claim.
That is, an objection weakens a claim, decreasing the probability that it is true. Strong objections considerably decrease the probability that the claim is true; weak objections only slightly decrease the probability.
Reasons and objections are analogous – reasons support claims, while objections weaken them. Or in other words, an objection to a claim is a reason in support of the rejection of that claim. For example, an objection to the claim that “Smith will win the election” will either be a reason to believe the claim that “It is not the case that Smith will win the election” or that “We don’t know if Smith will win the election“. As an objection is a reason against the conclusion, for ease of communication will often use the word “reason” to refer to both reasons for and against (i.e. objections).
Here Mary is objecting to what Bill says:
Bill: You should exercise regularly.
Mary: But exercising regularly takes up a lot of time, and you shouldn’t do things that take up a lot of time.
This argument contains a claim “You should exercise regularly“, and an objection made out of the two claims “exercising regularly takes up a lot of time” and “you shouldn’t do things that take up a lot of time“:
You can think of this objection as being an argument for the falsity of the claim, since it says that “You shouldn’t exercise regularly, because exercising regularly takes up a lot of time, and you shouldn’t do things that take up a lot of time”.
The same claim will often be both supported by a reason, and weakened by an objection. For example, we can add a reason to the example above to get this argument:
An objection often provides direct evidence that a particular claim is false. But sometimes an objection will just assert that we shouldn’t accept a claim, without thereby saying that we should reject it. That is, it may be an argument for suspending judgment about the claim:
So far, no cure for cancer has been found; if no cure for cancer has so far been found, we should suspend judgment about whether we will find one.
This objection does not say that we will not find a cure for cancer (i.e. it doesn’t say the disputed claim is false); it just says that we should suspend judgment.