Continuum fallacy

The (erroneous) rejection of categorizations on the grounds that the variations described can also be described as a continuum.

Take, for example, the following thought experiment, also known as the “heap paradox”:

A single grain of sand does not yet constitute a heap of sand.
Two grains of sand do not yet constitute a heap of sand either.
For any number of grains of sand that does not yet constitute a “heap”, one could argue that adding one more grain of sand would not make any difference.
No matter how often you add another grain of sand, it is difficult to argue that you now have a “heap” when you did not have one before.
Nevertheless, there is a quantity of grains of sand that most people would recognize as a “heap of sand.”

There is a continuum between the two states of “no heap” and “heap,” with no clear dividing line between these categories. Nevertheless, these states describe real phenomena and should therefore be distinguished from one another.

• Sorites fallacy
• Argument of the beard

If categories exist within a continuum and the boundaries between them are vague or inconsistent, it can be difficult to determine where one category ends and another begins. However, it only becomes a logical fallacy if one concludes from this that the categories do not exist or are irrelevant.

In many cases, it may make sense to allow for a “gray area” in which one simply accepts that a clear-cut determination is not possible. However, this can in turn lead to the problem of having to define the boundaries of this gray area. In this case, the problem has simply been shifted.

If a clear cutoff point is necessary, it can be established through an official authority. An example of this approach is defining the age of majority as of a specific date (in most Western countries, the 18th birthday). However, this too can lead to problems if the rule does not account for all special cases and exceptions (Accident fallacy).

Between two variations on a continuum, there may be further meaningful subdivisions: between white and red there is pink – and dozens of other shades, such as fuchsia, old rose, etc., which may only make sense in certain contexts (False dilemma).

Although the standard examples of this fallacy usually seem rather trivial and inconsequential, similar instances are not exactly rare in public discourse and are often the subject of heated debate. This is particularly true when it is the discussion is about finding the boundaries that define the threshold between categories.

Arguments like the following are often heard when someone tries to defend their own (usually unscientific) theory:

Even science can never provide perfect explanations.
That is why my theory is just as good as those of the sciences.

It is true that a significant part of scientific work consists of continually questioning even established positions and never assuming that any field of knowledge has been “fully explored”. It is precisely through this questioning that science has continued to develop and can today, in most cases, offer reasonably good explanatory models for many phenomena – but never “perfect” ones.

There really isn’t much to object to when new theories are put forward by people outside the scientific community – even if some scientists do indeed often seem to struggle with this. In fact, there are many examples of outsiders triggering important advances in the sciences.

However, one must also consider the possibility that a new theory – especially if it comes from outside the field and, perhaps even from someone who does not fully comprehend the complexity of the subject – is simply utter nonsense. This possibility represents, so to speak, the other end of the continuum.

Based solely on the above, it is not possible to determine whether the position being taken falls more on the “scientific” or the “nonsensical” side of this continuum. However, if the speaker feels it necessary to resort to such rhetorical tricks to defend it, this does not immediately cast the position in a favorable light.

If one views the political spectrum as a continuum from left to right (which should be noted is highly simplistic methodand is not always the most useful one), one finds a few extremists of both orientations at both ends of the spectrum and the vast majority of the population in the middle between these two poles.

Since there are few clearly defined points at which specific labels (including “far-left,” “social democratic,” “social liberal,” “neoliberal,” “conservative,” “far-right,” etc.) begin and end, one might conclude that there can be no distinction at all – and simply label any stance that lies to the left of one’s own position as “radical left” (often as “communists” or “anarchists”), or alternatively anything to the right of oneself as “far-right” (with “Nazi” or “fascist” serving as intensifiers).

In reality, most people on the conservative side of the political spectrum have little sympathy for actual Nazis, just as a social democrats do not necessarily have to be sympathetic to communism or even anarchism.

A fertilized (human) egg cell divides and initially forms a group of cells, from which an embryo eventually develops. However, it is not possible to clearly determine at what point it is merely a “cell cluster” or when it becomes an embryo.

In this context, it becomes clear that the mere assumption that there is no clearly definable transition from one state to another does not necessarily imply that there is no such transition.

However, this question is of central importance to the moral and legal assessment of abortions. It is therefore important that this issue be discussed without prejudice.

• False dilemma
• Mu

• Continuum fallacy on Wikipedia
• Sorites Paradox on Stanford Encyclopedia of Philosophy
• The Fallacy of the Heap on Fallacy Files
• Continuum fallacy on RationalWiki