Formally Valid Non Sequiturs?
One common conception identifies logical fallacies with arguments “that seem valid, but are not.” This definition is difficult to sustain however, because there are arguments so obviously fallacious that they would probably would not trick anyone with their “seeming validity.” While there are fallacious arguments that are invalid, there are examples of fallacious arguments that are valid, while others are even sound. In order to notice these examples, and identify their logical shortcomings, we need to use the tools of informal logic, not being content to let formal validity or formal fallaciousness decide the ultimate logical disposition of a given argument.
Formal Fallacies – Fallacies of Relevance?
What is wrong with this argument?
(P1) All collies are animals.
(P2) All dogs are animals.
(C) Therefore, all collies are dogs.
The astute observer will recognize this as a formal fallacy – that of “Undistributed Middle.” But suppose that we suspend our awareness of the nature of this argument’s logical defect and reexamine it from a different perspective.
Take, for instance, Govier’s ARG model of argument appraisal. According to this model, if the argument is a logical failure, then one or more of its premises will be:
- unacceptable (e.g., making dubious assumptions, lacking veracity),
- irrelevant to the conclusion, or
- insufficient to establish the conclusion.
What failing can we ascribe to the collie/dog argument? Obviously both premises are true (as is the conclusion). The problem with this argument is that the premises are irrelevant to the conclusion. Neither that collies are animals nor that dogs are animals counts in favor of collies being dogs.
Notice that in ascribing irrelevance to this argument, we have ventured beyond the purely syntactic, and are leaning on contextual considerations in order to assess its logical standing, just as we would for any other natural language argument whose logical structure can’t be parsed into a form whose validity or lack thereof we can recognize easily.
My suggestion is that while we continue to regard Undistributed Middle as a formal fallacy, why not also classify it as a fallacy of irrelevance?
Valid But Fallacious
Let’s take another example:
(P1) If Einstein was a genius, then all collies are dogs.
(P2) Einstein was a genius.
(C) Therefore, all collies are dogs.
The keen eye will notice the logical form of this argument immediately: modus ponens. It is a valid argument. In the context of argument evaluation, if we appraise an argument as formally valid, normally we just pack up and move on. The question I want to press is whether an argument can be logically fallacious even if it is valid. According to one definition of fallacy, the answer is a clear “no.” Specifically, if a fallacy is regarded as “an argument that seems valid, but is not” (Cf. C. L. Hambin, Fallacies) it follows immediately that a valid argument cannot count as a fallacy.
Again, let us suspend our awareness of this argument’s formal structure and look at it through the ARG lens. Is there a connection between Einstein’s being a genius and the nature of collies such that anything about the former would count in favor of the latter? If not, it seems inevitable that, again, we have to appraise the premises of this argument as irrelevant to its conclusion, despite the argument’s validity. This argument is a non sequitur. I contend that “non sequitur” names the fallacy associated generically with the failure of an argument’s conclusion to be supported due to irrelevant premises. The term “non sequitur” can apply to either informal or formal fallacies.
What the foregoing observations serve to show is that a quick assessment of an argument as formally fallacious or formally valid can preempt assessment of the argument using the criteria of appraisal of informal arguments – criteria that incorporate contextual awareness – that can render more useful verdicts about an argument’s logical standing.
In particular, a formally valid argument with contextually irrelevant premises can be regarded as a non sequitur, i.e., it can be regarded as a logically fallacious argument despite its formal, syntactic validity.