"An argument may be refuted either by a counter-syllogism or by bringing an objection. It is clear that counter-syllogisms can be built up from the same lines of arguments as the original syllogisms: for the materials of syllogisms are the ordinary opinions of men, and such opinions often contradict each other. Objections, as appears in the Topics, may be raised in four ways -- either by directly attacking your opponent's own statement, or by putting forward another statement like it, or by putting forward a statement contrary to it, or by quoting previous decisions."
~Aristotle's Rhetoric, Book 2, Chapter 25
Little attention is given to the 'art' of refuting arguments in most Critical Thinking or Logic courses. Some professors of these disciplines never treat refutation at all leaving their students to master this elegant art on their own. Consequently, few students ever become proficient in refuting arguments until and unless they move on to graduate studies in their discipline. This is unfortunate. Argument refutation is the highest expression of a well disciplined critical thinker or logician. Aristotle was of the view that refutation by logical analogy was the ultimate level of human intelligence. His reasons are simple and direct.
First, even the prospect of refuting an argument entails understanding that argument at every level of its definitional meaning and logical implications.
Second, formulating a refutation of any argument is a grueling task that requires all the faculties of the intellect to work harmoniously to a single purpose. A full and rich understanding of the nature of common fallacies, vague and ambiguous definitions of terms, and the limits of any body of evidence is required for any successful refutation of an argument. All of one's general back ground knowledge, critical thinking skills, intellectual abilities, personal interests and temperaments are in play when successfully refuting an argument.
Lastly, and most importantly, successful argument refutation arises out of, and culminates in, an aesthetic appreciation of both intellect and intuition. That is to say, successful argument refutation requires an understanding of the limits of both intellect and intuition that is only elegantly achieved in the awareness that neither intellect nor intuition can be relied upon completely alone to produce sound reasoning. Only when all elements of intellect and intuition combine seamlessly does a refutation ascend to the level of beauty.
Taking these three reasons as a starting point for the study of refuting arguments, all arguments, be they formal or informal, can be refuted in several ways. They can be grouped in four main divisions. Given that one understands that the very nature of any argument is a set of premises entailing a conclusion by logical necessity, one can begin to refute any argument. For to 'refute' any argument means to demonstrate that its premises do not entail its conclusion by logical necessity.
1. Refute the Logic:
Informal Arguments: Many informal arguments appear rhetorically convincing. Yet, upon close examination, these arguments commit common informal fallacies of irrelevance, presumption, and/or ambiguity. Chapter 2 in our course study provides more than adequate explication of how to recognize informal fallacies. For, if any informal argument can be shown to contain irrelevancies, presumptions, and/or ambiguities, then that argument is effectively refuted.
Formal Arguments: More difficulty in refutation is presented by arguments that violate known VALID FORMS of reasoning. In Aristotelian Categorical Logic, a complete understanding of the nature of ‘term distribution' is fundamental to recognize when the terms in the premises of an argument are not sufficiently 'distributed' to entail the conclusion by logical necessity. Chapters 5, 6, and 7 in Copi, Cohen's, Essentials of Logic provide more than adequate explication of how to recognize formal fallacies. For, if it can be shown that any formal argument violates a proven VALID FORM of reasoning, then that formal argument is effectively refuted.
In modern Symbolic Logic, also know as Propositional or Predicate Logic or even Sentential Logic, a complete understanding of the logic of language 'syntax' and 'grammar' is required to recognize when 'statement claims' themselves necessitate inferences by logical entailment. Chapters 3 and 4 in our course study provide more than adequate explication of how to recognize sentence structure formal fallacies. For, if it can be shown that any formal argument violates the very rules of syntactic or grammatical structure, then that formal argument is effectively refuted.
2. Refute the Definition of Terms: Both informal and formal arguments may indeed have their conclusions entailed by their premises through logical necessity and therefore be valid. Yet, the terms used in these arguments fail to adequately account for significant 'distinctions' between and among the terms. Or, these definitions may be too shallow, in that they fail to account for underlying assumptions that themselves need to be proven before the definitions can be accepted as factually 'plausible'. Definitions with unexamined assumptions result in arguments that either 'over-simplify' the issue under debate or 'over-generalize' the issue under debate. Thus, either too much or too little is claimed by these arguments making them easily refuted often by making a simple distinction. Chapters 5 in our course of study provides more than adequate explication of how to recognize inadequate definitions and replace them with precise definitions. For, if an argument, however valid, hinges on imprecise definitions that fail to resolve underlying assumptions, then that argument, for all its' validity' remains 'unsound' and is thereby refuted.
3. Refute the Evidence for the Premises: Often very convincing arguments are made from a limited body of evidence that supports some underlying set of unexamined presumptions. These presumptions themselves can blind the investigator to only look for, and find, evidence that supports their pre-conceived point of view while ignoring any contrary or even contradictory evidence against that point of view. Since humans most often extend formal arguments in order to support some pre-conceived, political, social, religious, or even philosophical pre-conception, an effective way to refute an argument is to cite factual counter-instances to the premises in the original argument. Moreover, unlike deductive validity that yields necessary truth, inductive, empirical testing only yields a range of 'probable truth'. This probable truth is always susceptible to more empirical testing, and hence there is always a likelihood of new evidence emerging that refutes earlier findings. Chapters 8, 9, 10, and 11 in our course of study provide more than adequate explication of the nature, power, and limits of inductive evidence, analogical reasoning and ethical assumptions when used to support the truth of premises in any formal argument. For, if even a valid argument, has premises that do not take full account of all available evidence, then those premises are suspect, and therefore the entire argument is suspect and effectively refuted by new evidence.
4. Refute by Contrary Argument: Most artful of all methods of argument refutation is refutation by counter-argument, or 'refutation by analogy'. Given that a particular argument is flawed, in any of the aforementioned ways, then constructing a new argument of the SAME FORM as the original, but having an obviously absurd flaw, is a stunning way to refute any suspect argument. Chapter 10 in our course of study provides more than adequate explication of how effective refutation by logical analogy can reveal hidden defects in otherwise appealing valid arguments. For, if an argument, however attractive to eager listeners, can be shown by analogy to have some structural defect then that argument is effectively refuted.
Links and Citations:
Full and complete reading of Aristotle's Sophistical Refutations (refutations that appear to be so, but are actually fallacies themselves).
One especially useful citation from Aristotle's Topics, Book II is the following. Enjoy its' richness:
"If you are not well equipped with an argument against the assertion, look among the definitions, real or apparent, of the thing before you, and if one is not enough, draw upon several. For it will be easier to attack people when committed to a definition: for an attack is always more easily made on definitions. Moreover, look and see in regard to the thing in question, what it is whose reality conditions the reality of the thing in question, or what it is whose reality necessarily follows if the thing in question be real: if you wish to establish a view inquire what there is on whose reality the reality of the thing in question will follow (for if the former be shown to be real, then the thing in question will also have been shown to be real); while if you want to overthrow a view, ask what it is that is real if the thing in question be real, for if we show that what follows from the thing in question is unreal, we shall have demolished the thing in question."