Broadly speaking, the construction of scholarly argument can be divided into two principle components: affirmation and refutation. Whereas the former asserts a certain point (i.e. "this is so"), the latter disputes a certain point (i.e. "this is not so"). In deconstructing an argument we are taking apart a counter-view and are accordingly concerned with refutation. While such refutation can take many forms, there are certain helpful critical guidelines we may follow.
First of all we should consider that "argument" does not simply mean "disagreement" but in fact has a specific technical definition within academic discourse. So understood, an argument denotes a set of propositions, including premisses and a conclusion, the latter following logically from the former. Hence the first line of advance in deconstructing an argument is to consider whether the premisses at work are sound or unsound. Logically enough, the result of this enquiry will tell us whether or not the conclusions derived from said premisses are valid or invalid.
In deconstructing a formal argument we want to reverse engineer the internal logic at work. Thus we can work backward from a conclusion to its premisses and verify whether they are sound or not. Consider the following argument: "If a nation is at war, it is because it has a strong military. Many nations are currently at war. All nations currently at war must therefore have strong militaries". The conclusion is at fault because the first premise, on which it depends, is demonstrably false. Nations with weak militaries may be attacked by militarily stronger nations and thus be forced into war regardless. In this instance, then, we could deconstruct the argument by underlining the dependency of the conclusion on the first premise, and then demonstrating why that premise is false. If we can falsify the premise, the conclusion necessarily becomes invalid.
Things get a touch more tricky when an author's premisses are sound but their conclusion invalid nonetheless. As an example, consider this argument: "I wake up every morning. The sun rises every morning. Therefore the sun rises because I wake up." Here we have two sound premisses: I wake every morning; the sun rises every morning. And we have one conclusion: the sun rises because I wake up. Now, this conclusion is clearly unsound. Not because premisses are in error but because the reasoning is fallacious. This is an example of False Correlation or cum hoc ergo propter hoc (with therefore because of). Just because two events happen to coincide it does not mean they were causally related; it is simply a coincidence.
Now that you are equipped with the critical tools to deconstruct an argument, you need to approach the task with a broader and methodical outlook. It is useful to see an academic text as possessing a kind of architectural integrity; its various discursive strategies are like pillars and beams. If you can identify critical weak links in the structure then you can pull them apart; this will, in turn, compromise the integrity of the argument in its entirety. Because a solid argument depends upon each of its constituent parts being coherent and contiguous, you may want to do a point-by-point refutation of the opposing argument, unravelling it piece by piece. On the other hand, you may want to locate a fundamental flaw in the text's underlying logic (this would most likely take the form of a false premise), and show how this undermines the rest of the work. There are numerous different approaches. The important thing here is to be consistent.
When deconstructing an argument, you want to ensure you maintain a coherent, logical methodology throughout. If your own argument is not water-tight then you are not in any position to refute anyone else's views. On this note, it is wise to be transparent about your methods. In deconstructing an argument, explain the processes you are using. For instance, you should overtly identify the disputed "premisses" and "conclusions"; explain how and why the one effects the other. You want to let the reader know your methodology of refutation. Further, you would highlight any logical fallacies you find, by name. This evidences further reading and analytical insight and will gain you marks in evaluation. Because you will repeatedly be using the same processes, of testing premisses for validity, you will quickly internalise them. With time, these skills will become fine-tuned and you will find it increasingly easy to take an argument apart, a valuable ability, which you will be able to apply across the board in scholarly work.
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