Standardising Arguments
So far, we have covered how to recognize argument, now we are going to look even closer at the structure of arguments. Standardising is a process that helps us examine an argument’s structure by formatting it in a way that makes it easy for us to see. There are different ways to standardise, and the one you choose is arbitrary, but I am going to demonstrate and use the way I was first shown because it is easy and less errors occur than using other methods. The process of transforming natural language to standard form can be difficult because some people do not write or speak in a straightforward manner at all. Issues to do with vagueness as we have discussed before can also be hazardous, but having a method makes it much easier.
The goal of standardising is to convert some natural language into a form that looks something like the following…
1. Premise 1
2. Premise 2
Therefore,
3. Sub-conclusion
4. Premise 3
Therefore,
5. Main Conclusion
We call this standard form. The form need not be exactly like this of course. There can be any number of premises (as long as there is at least one) and any number of sub-conclusions (even 0). This is a general example to illustrate the type of structure that we would like to see our argument in. The exact way that the argument is displayed and the notation is somewhat arbitrary, this is just a way of making arguments easier to read.
An example argument…
“There exists a mind that has produced nature; for nature exhibits complexity, order, beauty and purpose. Nature was either produced by accidental processes, or by an intelligent mind. The features we see are too beautiful to be explained by mere accident.”
So, how do we get this into standard form? We first identify the statements within the argument, separate them, and assign them a letter of the alphabet. We can show which part we are referring to by enclosing the statement in angled brackets. After that, we underline the inference indicators, because these give us crucial information about the structure of an argument.
It will look something like this…
(a) <There exists a mind that has produced nature>; for (b) <nature exhibits complexity, order, beauty and purpose>. (c) <Nature was either produced by accidental processes, or by an intelligent mind>. (d) <The features we see are too beautiful to be explained by mere accident>.
I have given the statements letters in the order that they appear. This just makes it simpler to follow what is going on. In the above example, you can see I have underlined ‘for’, because it is an inference indicator that tells us what comes before it is inferred from what comes after it. We can then put the argument into standard form, which would look something like this…
(b) Nature exhibits complexity, order, beauty and purpose
Therefore,
(d) The features we see in nature are too beautiful to be explained by accident
(c) Nature was either produced by accidental processes, or by an intelligent mind
Therefore,
(a) There exists a mind that has produced nature
So, we have changed the order from the grammatical order to the logical order and the form of the argument is more clear. This was a fairly easy example but of course some arguments are much harder in their original form so standardising gives you a big advantage in working out how the argument is structured.
I will give you a few rules for standardising arguments.
- Conjunctions should usually be split up and a letter assigned to each conjunct, because when you assert a conjunction, you are asserting that each of the conjuncts is true.
- Disjunctions should not be split up, because you are not asserting that each of the disjuncts is true, you are asserting the entire disjunction.
- Conditionals should not be split up because you are not asserting the antecedent or the consequent, only the conditional as a whole.
- Modal expressions that are acting as inference indicators needs to be replaced by non-modal expressions. Other modal expressions may remain but make sure they are not being conflated if the same one is being used more than once.
- Pronouns should be replaced by what they are referring to. Pronouns are often fine when in context, but since standardisation removes context they can be confusing. Such words that need translation are ‘his’, ‘my’, ‘it’, ‘this’, that’ etc.
- Omit any material that is extra commentary, background info, or merely setting the context.
- If the same assertion is made more than once, use a single letter for both.
- Ignore stylistic or personal phrases such as “In my opinion”
In general, each item in a standardised argument should be one complete assertion; no more and no less. This can be part of the original text, or a conversion of that text that retains the same meaning.
Missing premises are something that can be tough to deal with when standardising argument. It is often the case that things are left out because they are simply obvious, but sometimes the things that are left out can be controversial. You should include missing premises when you standardise, but only those that are absolutely necessary. Do not make the mistake of putting words in someone else’s mouth unless you are sure that it is required for their argument. There will often be more than one way to fill the gaps in someone’s argument; always do it in the way that makes their case the strongest. The principle of charity is very important because if you make someone’s argument weaker than it needs to be, they can simply disagree with the missing premise that you included and you have wasted your time. Also, you are not getting any closer to the truth by arguing against a weaker argument.
The all-purpose premise is one that magically fills any gaps in reasoning. If I had an argument of the form “A, therefore B” and it seemed like there was some gap between A and B, I may be tempted to include an extra premise so that the argument read like A; If A, then B; Therefore, B. This would appear to have bridged the gap in the original argument, but in fact it has done no such thing. In the original, there was some gap between A and B, so in the premise ‘If A, then B’ the same gap would exist, so we have just moved the problem from the argument structure to one of the premises. Begging the question is the name we give this fallacy, and it can be summarised by defining it as assuming the conclusion of an argument in its premises.
A few examples…
Here is an argument that I will standardize to demonstrate some of the principles outlined above.
“Ted took Peter and Paul to the zoo. Peter was hoping to see a lion or tiger. If Paul did not see a giraffe, he would have been unhappy. Paul saw a giraffe. It follows from this that he was happy. Peter saw a lion. Peter must have been happy. I think that taking them to the zoo was a great idea.”
This seems rather simple, but it will demonstrate most of the principles that we have talked about in standardisation. This is what it looks like with the premises identified and inference indicators underlined.
(a) <Ted took Peter and Paul to the zoo>. (b) <Peter was hoping to see a lion or tiger>. (c) <If Paul was unhappy, it would be because he didn’t see a giraffe>. (d) <Paul saw a giraffe>. It follows from (d) <this> that (e) <he was happy>. (f) <Peter saw a lion>. (g) <Peter must have been happy>. I think that (h) <taking them to the zoo was a great idea>.
Let us have a look at each part in more detail.
(a) <Ted took Peter and Paul to the zoo>
You are probably thinking “that’s a conjunction, you need to separate it!”. I thought I would throw this in to illustrate a different point. Usually, conjunctions are separated into two items for your standardised argument. For example “Stef lives in Canada and Greg lives in the US” would be broken up into “Stef lives in Canada” and “Greg lives in the US”, so why did I not do that here?
Well, sometimes conjunctions are saying more than what is immediately obvious. If I was at a ball and commented “John and Grace are dancing”, would this mean the same thing as “John is dancing” and “Grace is dancing”? It would not, because I am actually saying that John and Grace are dancing together. Similarly, if I were to say that Stef and Christina are married, and break that down into two statements, I would be missing the meaning I was trying to convey in the first place; that they are married to each other.
In our example, it is quite reasonable to assume that Ted took both Peter and Paul to the zoo together, so we can leave this as one complete statement because separating it would be losing some of the meaning.
(b) <Peter was hoping to see a lion or tiger>
This is a disjunction, and we cannot separate it because neither of the disjuncts is being asserted, only the disjunction as a whole.
(c) <If Paul was unhappy, it would be because he didn’t see a giraffe>
This is a conditional, and as neither the antecedent nor consequent is being asserted, we cannot break them up.
(d) <Paul saw a giraffe>
A simple declaration.
It follows from (d) <this> that
What is going on here? There is obviously an inference indicator, but there is something else going on too. ‘this’ is acting as a pronoun, representing the previous statement, so we treat is as such and give it the same letter as the previous statement. This is equivalent to “It follows from the fact that Paul saw a giraffe that…”
(e) <he was happy>
This is also a simple declaration, but it contains a pronoun. When we translate this we must replace ‘he’ with what ‘he’ is referring to, in this case; ‘Paul’.
(f) <Peter saw a lion>
Another simple declaration.
(g) <Peter must have been happy>
This is a declaration with a modal expression inside, acting as an inference indicator. ‘must have been’ is showing us that the sentence is a conclusion. We will translate this to “Paul was happy” because that is the meaning of the sentence.
I think that (h) <taking them to the zoo was a great idea>
In this sentence we ignore the start because it is simply stylistic. It could be the case that an expression such as ‘I think that’ could form part of a declaration, but here the declaration is about how the idea was great. We also need to convert the pronoun ‘them’ to what it represents; ‘Peter and Paul’.
So, what does this all look like?
(a) Ted took Peter and Paul to the zoo
(c) If Paul did not see a giraffe, he would have been unhappy
(d) Paul saw a giraffe
So,
(e) Paul was happy
(b) Peter was hoping to see a lion or tiger
(f) Peter saw a lion
So,
(g) Peter was happy
So,
(h) Taking Peter and Paul to the zoo was a great idea
We have a clearer understanding of the structure of the argument being put forward now, but we can take it one step further. It is not always clear which conclusions follow from which premises or how they follow. I will introduce a simple method of showing where and how inferences have occurred, and this will round out our standardisation procedure for now.
The first step is notation; we will use square brackets at the end of each line in our argument to contain the information about that part of the argument. We are going to denote a basic premise with [prem]. [prem] is only used when no inference has been made to the premise, so sub-conclusions will not get this tag. For inferred statements, we will include in square brackets the letters representing the premises that the statement was inferred from.
An example…
(a) Socrates is a man [prem]
(b) All men are mortal [prem]
So,
(c) Socrates is mortal [a, b]
There is just one more bit of detail that we are going to include at this stage, and this is when a statement is inferred from two or more other statements. When this happens, we will specify how the other statements combine to support the inferred statement.
Linked statements are when two or more statements do not, on their own, support the conclusion, but do so when combined. Convergent statements are when two or more statements each lend support independently to a conclusion.
In the above example about Socrates, it is clear that the two premises only support the conclusion when they are combined. On their own they lend no support to the conclusion. We would denote this as so;
(c) Socrates is mortal [a, b, linked]
I will now revisit the argument about Peter and Paul with all of the information filled in.
(a) Ted took Peter and Paul to the zoo [prem]
(c) If Paul did not see a giraffe, he would have been unhappy [prem]
(d) Paul saw a giraffe [prem]
So,
(e) Paul was happy [c, d, linked]
(b) Peter was hoping to see a lion or tiger [prem]
(f) Peter saw a lion [prem]
So,
(g) Peter was happy [b, f, linked]
So,
(h) Taking Peter and Paul to the zoo was a great idea [e, g, a, linked]
We could also make the above argument more precise by including “..at the zoo” after all the premises about Peter and Paul, but I left it out for ease of reading.
So, this concludes the procedure for standardising arguments. We can now recognize argument, identify different parts of an argument, and rewrite the argument in a way that allows us to look at the overall structure. This is certainly the most cumbersome part of the process of argument evaluation. In the following articles we will start looking at the insides of the argument; both in the reasoning between statements, and the truth of the statements themselves.