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This page offers a brief explanation of how to analyse the mechanics of arguments and objections.
It starts with an overview of some important terms, and then goes through the various steps necessary when analysing arguments:
Firstly, we need to establish what the central claim is in the argument. What are we arguing about?
Secondly, we need to map the various arguments. Is this an argument for a claim or against it, or is it an objection to another argument? and so on.
Thirdly, we need to reconstruct the first argument in the chain. This enables us to properly see how it works, and how the various key ideas connect together.
Fourthly, we should then be able to see exactly how the objections hope to undermine this argument. We then do the same with responses to these objections and so on.
Finally, we need to look at what our chain of arguments shows - and be careful not to over sell what we have done.
Stage 1. Identifying the central claims, conclusions, propositions and premises
Stage 1. Identifying the central claims, conclusions, propositions and premises
A debate should be focussed around one central claim. That claim may have a name, like direct realism, or just be a sentence like, schools should not enforce a school uniform.
People will then make arguments to support or attack that claim:
Arguments are made up of premises (or reasons) and conclusions:
Premise 1: If I’m in Valencia, then I’m in Spain.
Premise 2: I am in Valencia.
Conclusion: ∴ I am in Spain
If there are no premises, no reasons, or justifications, for the conclusion, then it is not an argument, it is merely an assertion.
Normally, an argument is made up of lots of sub-arguments with sub-conclusions, all linked together. But hopefully, you will be able to pick out critical sub-arguments from the whole.
Technically, a proposition is what is expressed by premises and conclusions.
Not every premise is always explicitly stated - there may be hidden premises, or assumptions. If an objection relies on an assumption, then you should be able to show how that links to the argument, and normally it is best to make it explicit when you outline the argument in the first place.
Stage 2. Mapping the arguments
Stage 2. Mapping the arguments
Once we have established what the central claim is, we need to map out the various arguments and see how they relate to that central claim.
An argument may be for or against a claim, or it maybe an objection to another argument or a response to an objection etc. The claim that an argument is for or against may only be a premise in another argument for another claim.
Our first task, when analysing argument is to be able to place the argument in the grand scheme of the debate.
Here is a diagram showing a simplified outline of how arguments might relate to a claim.
In reality, the argument scheme on a particular topic is more likely to look like the picture below rather than the picture above. In everyday life, the hardest thing can be placing the argument in the chain, and establishing how it is relevant to the central claim of a discussion.
We must respond to an argument with an objection to that argument and not with an argument against the claim. For example, looking at the diagram, you can’t object to argument A using Argument B. Formally, this is a kind of ignoratio elenchi - which means 'ignoring refutation'. In effect, your argument is irrelevant at that point in the discussion and thus you are ignoring the rules of refutation. If you do this in the essay, the examiner will say that you are merely juxtaposing arguments rather than engaging in the dialogue.
Similarly, people often think they are arguing against a claim, when they are in fact objecting to an argument for a claim. This can be a reasonable thing to do, but you must first reconstruct the argument that you are objecting to. And you must reconstruct it in the strongest terms (according to the principle of charity) otherwise you are guilty of creating a strawman.
Stage 3. Reconstructing the arguments
Stage 3. Reconstructing the arguments
Once we have our maps showing the chains of arguments, we now need to reconstruct the main argument in each chain. This is perhaps the most difficult part of the process. What we have to do is identify the main premises and the conclusion and sub-conclusions and see how they all fit together.
The first thing to do is work out what kind of argument it is, and then we need to investigate the way that the premises hang together - the logical connections.
Kinds of arguments
Arguments can be deductive, inductive or abductive. Broadly speaking the differences can be seen in the following table:
Deduction
What must be the case
If p then q
p
∴ q
Induction
Generalising from a particular case
p
q
∴ If p then q
Abduction
Inference to the best explanation
If p then q
q
∴ p
In a deductive argument, the conclusions are necessary (not contingent). A logical deductive argument is valid. A logical deductive argument with true premises is sound.
In inductive and abductive arguments, the conclusions are probable, contingent, plausible. The logic of an inductive argument is strong or weak. If the argument is strong and the premises are true, then the argument is cogent.
Of course, deductive, inductive, and abductive arguments can come in forms other than those described above. For example, a common kind of inductive argument is an argument from analogy:
X is A and B.
Y is A.
∴ Y is B.
Another common kind of inductive argument is a wager or game theoretic argument
Either A or B
Either X or Y
∴ Either A and X, A and Y, B and X, or B and Y
[Rank the four possibilities]
Logical connections
In a deductive argument, it needs to be possible (at least in principle) to show how all the premises link together, even if you don’t make every premise explicit.
In deductive arguments, there are two main ways of relating one premise to another: Term Logic, and Propositional Logic
Term Logic
This kind of relation is based on individual terms or phrases within a clause. It’s a bit like solving equations through elimination or cancelling. You need two premises which you connect together by eliminating shared terms. E.g.
Dave runs
To run to is to go quickly by moving the legs more rapidly than at a walk
∴ Dave goes quickly by moving his legs more rapidly than at a walk
But be wary of quantitative terms, e.g. all, some, no etc.
Some examples:
Some teachers are not nice
All teachers are animals
∴ Some animals are not nice
No homework is fun
All philosophy essays are fun
∴ No philosophy essays are homework
Propositional Logic
The basic unit here is a proposition (or clause). Propositions are connected together with conditional statements. There are three main types of conditional that we are concerned with:
If p then q/p only if q
This is called an material conditional.
Here, p is the antecedent and q is the consequent.
‘If’ is a marker of a sufficient condition. ‘Only if’ or ‘then’ or ‘must’ is a marker of a necessary condition. (And ‘if and only if’ is a marker of both.)
Either p or q
This is called a disjunction. When doing philosophy, we often distinguish between an exclusive disjunction and an inclusive disjunction. An exclusive disjunction is when p and q cannot both be true at the same time. An inclusive disjunction is when they can.
Not both p and q
This is sometimes known as an alternative denial.
It is important because it often implies some kind of contradiction between p and q.
And we use these conditionals to form arguments. The argument forms we come across most frequently are:
Modus Ponens: If p then q, p, ∴ q
Modus Tollens: p only if q, not q, ∴ not p
Disjunctive syllogism: either p or q, not p, ∴ q
Exclusive syllogism: not both p and q, p, ∴ not q
Hypothetical syllogism: if p then q, if q then r, ∴ p then r
Stage 4. Analysing the objections and responses
Stage 4. Analysing the objections and responses
Normally, it’s not necessary to formally reconstruct objections or responses to objections. Instead, we just need to focus on exactly how the objection attacks the argument.
(Note. these can also be useful when analysing arguments against a claim.)
We can remember five of the most common ways of objecting to an argument with the acronym FAILS:
False premise
Argument is invalid
contradictory Intuition,
Ludicrous conclusions
Speculative conclusions.
If we are explaining the mechanics of an objection, we would say something like 'this objection attempts to undermine … [the claim/argument/etc] … by arguing that … '
F
The argument or claim rests on a False premise/assumption.
There are two ways in which an argument can be false.
A conditional premise might be disproven with a counter example:
E.g. we can show that the conditional, if p then q, is wrong (i.e. p is not sufficient, or q is not necessary) by coming up with an occasion when p is true but q is not.
We can show that, either p or q, is wrong (i.e. the disjunction is not exhaustive) by coming up with more options.
An assertion, assumption, can shown to be false on the grounds that:
There is contradictory evidence (if it is an empirical claim [or matter of fact])
It is self-contradictory or nonsensical
Or, you may accept a particular framework (e.g. Hume’s fork) and show that it is false within that framework - i.e. not a relation of ideas etc.
A
The Argument is invalid (or weak if it is inductive/deductive). There are many reasons why an argument may be invalid:
The conclusion doesn’t follow from the premises - there is a logical leap (a non sequitur) This is when you cannot work out how to get from the premises to the conclusion (either using term logic or propositional logic)
The argument commits some fallacy: is circular, equivocation, affirms the consequent, denies the antecedent, confuses a necessary for a sufficient condition or vice versa etc.
The argument is inconsistent - i.e. one of the premises contradicts another.
The argument is weak against some inductive standard:
Ockham’s razor - do not invoke too many entities. If you have to invent something to make it work, that’s a problem. (Fewer moving parts/things is better)
Law of Parsimony - the simplest explanation is the best. (Fewer steps is better)
Sagan standard - Extraordinary claims require extraordinary evidence.
If the argument is abductive, then it can be shown to be weak by demonstrating that there are many other equally or more plausible explanations.
If the argument is from analogy, then it can be shown to be weak because it is arguing from one (or too few) cases.
I
We have a competing or contradictory Intuition/idea. This is when there is a proposition which appears to contradict the conclusion.
L
The conclusion of this argument is absurd/leads to absurd consequences. This kind of objection is called a reductio ad absurdum [Ludicrous]
S
The conclusion of this argument is impractical, unusable, unverifiable, unfalsifiable. [Speculative]
Stage 5. Establishing conclusions and weighting (What have you actually shown?)
Stage 5. Establishing conclusions and weighting (What have you actually shown?)
When you’re concluding a section or the essay, you need to think about what you have actually shown (not what you want to have shown). It doesn’t matter if your conclusions aren’t particularly strong or clinching. You mustn’t say you’ve proven something when you haven’t.
If there is a false premise/invalid argument/absurd conclusion - then the argument for the claim is unconvincing. However, whilst the argument for the claim may be unconvincing, there may be other more convincing arguments for it.
If there is a competing intuition, then it might be possible for the argument to either incorporate that intuition, show that it’s not actually a contradiction (or simply dismiss it as wrong using a Moorean shift: In a Moorean shift, you accept the underlying assumption, but deny the consequent - turning a Modus Ponens into a Modus Tollens:
From...
If this competing idea is true, then this argument is wrong
This competing idea is true
∴ the argument is wrong
To...
If this competing idea is true, then this argument is wrong
This argument is not wrong
∴ this competing idea is not true.
If the argument is shown to be absurd, this could also be dismissed with a Moorean shift.
If the argument is impractical - this will only matter if the argument is trying to be practical or needs to be practical.
If the argument for the claim is convincing, then it is clinching
An argument for a claim may fail, but that does not necessarily mean that another argument for it may succeed.
It may be possible to defend an argument against objections, but we cannot rule out that another objection that we haven’t considered may succeed. But, if you have considered the most famous objections, this may count as good reason for supporting the claim.
An argument against a claim may succeed, in which case it will be a clinching argument.
An argument against a claim may fail, but we cannot rule out the possibility that other arguments against it may succeed.
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