Continuum fallacy:

Definition Example
When an argument is rejected on the grounds that one of it’s concepts cannot be rigorously defined discretely and placed into a precise category. You can’t claim that your backpack is heavy until you tell me at what weight something becomes “heavy.”
Also known as: fallacy of the beard
  Notes
This fallacy is technically committed when a claim is rejected because a concept within the claim is, to some degree vague. Many concepts are intrinsically gradient such as like/dislike, child/adult, cold/hot, belief/disbelief, and intelligent/unintelligent. It can be admitted that an isolated term such as “unjust” both 1) vaguely covers various degrees of injustice, and 2) has semantic significance. Ideally, those wishing to effectively communicate a concept that is intrinsically gradient will include modifiers that indicate where on the gradient the current invocation of the term belongs. For example, instead of simply saying “unjust”, one can attempt to convey a greater semantic resolution by saying “rather unjust”, “horribly unjust” or “just as unjust as X”.

Case Study One

One common example of the continuum fallacy is in a scenario in which one must determine what constitutes “evidence” or “proof” for a given proposition. If someone claims to be able to accurately predict coin flips, for example, just how many consecutive correctly predicted flips would constitute evidence (beyond statistical noise) for the claim? And how many flips would constitute proof of this ability? The take-away caveat is that we need to define our terms as rigorously as possible, and not try to treat concepts that are intrinsically gradient as if they represent granular categories.


Case Study Two

Imagine you claim a client took “too long” to deliver a product. The fact that “too long” is subjectively or conventionally defined does not mean the term has no semantic significance.


Case Study Three

If your doctor tells you that you are “overweight”, and need to slim down a bit, it would make little sense to argue that the concept “overweight” has no clear demarcation, and therefore you need not heed his advice.


Keep in mind that a fallacious argument does not entail an erroneous position.


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