Continuum fallacy

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

The classic example of this fallacy is the following thought experiment, also known as the “pile” or Sorites-paradox:

A single grain of sand does not yet constitute a pile of sand.
Nor do two grains of sand make a pile of sand.
For any number of grains of sand that do not yet form a “pile”, one could argue that adding one more grain of sand would make no difference either.
No matter how often you add a single grain of sand at a time, it is difficult to argue that you now have a “pile”, whereas without it there was still no pile.
Nevertheless, there is a quantity of grains of sand that most people would recognise as a “pile of sand”.

There is a continuum between the two states “no pile” and “pile”, with no clear criterion for distinguishing between them. Nevertheless, these two states represent meaningful categories and should therefore be treated as different.

• Sorites fallacy
• Argument of the beard

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

To put it another way: since there is no clear boundary between A and B, they are not regarded as separate categories – even in a situation where it would make more sense to view them as such.

There may be further meaningful subdivisions between two variations on a continuum: for example, between white and red lies pink, and there are numerous other shades such as fuchsia, old rose and so on, which may only be meaningful in certain contexts.

Similarly, in other contexts too, there may be more than exactly two categories, between which there are continua that make it difficult to distinguish between them.

The term “false dilemma” refers to a situation in which there only seems to be a limited number of choices (typically exactly two), even though there are in fact more options available.

At least in certain cases, this therefore describes the complementary mistake to the continuum fallacy: whereas the latter dissolves categories, the “false dilemma” constructs them artificially.

In many cases, it may be sensible to allow for a “grey area” in which one simply accepts that it is not possible to establish a clear distinction. However, this can in turn give rise to the problem of having to define the boundaries of this grey area. In such cases, the problem has simply been shifted.

If a clear boundary is required, it can be set by an authority. An example of this approach is setting the age of majority as 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 (see also: Accident fallacy).

Although the standard examples for this fallacy seem rather trivial and of little significance, similar patterns are by no means rare in public debate and are often the subject of heated discussion. This is particularly the case when it is necessary to establish boundaries that define the transition.

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 an essential part of scientific work involves constantly questioning established views and never assuming that a field of knowledge has been “fully explored”. It is precisely through this process of questioning that science has continued to develop and is now, in most cases, able to offer reasonably good explanatory models for many phenomena, though indeed never “perfect” ones.

In principle, there is also little to object when new theories are put forward from outside the scientific community – even if this idea is sometimes difficult for some scientists to embrace. Indeed, there are many examples of outsiders bringing about significant advances in the sciences.

On the other hand, however, one must also consider the possibility that a new theory – particularly if it comes from outside the discipline and perhaps from someone who cannot really appreciate the full complexity of the subject – is simply utter nonsense. This possibility represents, so to speak, the other end of the continuum.

There is no clear dividing line on this continuum between “scientific perfection” and “pseudoscientific nonsense”, but that does not mean that a distinction is impossible or even arbitrary.

On the basis of the statement above alone, it is also impossible to determine whether the position put forward lies closer to the “scientific” or the “nonsensical” end of the spectrum. However, if the speaker feels the need to resort to such rhetorical sleight of hand, this does not, at first glance, cast the position in a favourable light.

If one views the political spectrum as a continuum from left to right (which should be noted is highly simplistic method and 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 fertilised (human) egg cell divides and initially forms a cluster of cells, from which an embryo eventually develops. However, it is not possible to determine precisely up to what stage this is merely a ‘cluster of cells’ or from what point onwards it is a human embryo.

However, such a provision would be important for the legal (and moral!) assessment of abortions. Clearly, a human embryo is far more deserving of protection than a cellular structure that merely has the potential to develop into one.

However, as with the age of majority, the transition between the two categories can only be determined by social convention or legal provisions. In most countries where abortion is legal, this threshold is typically reached around the third month or twelfth week of pregnancy. Such provisions are just as arbitrary as those for the age of majority and are sometimes handled differently in other countries.

However, one commits a fallacy when one concludes, from the impossibility of pinpointing a precise moment of transition between these states, that no such transition exists. This fallacy can be found on both sides of the societal debate – whether one side sometimes attempts to define the beginning of human life as occurring at the moment of nidation (the implantation of the fertilised egg in the womb), or, in some cases, even to the moment of fertilisation of that egg – or whether the other side seeks to deny human status to all unborn life, in extreme cases right up to the moment of birth.

Both are extreme positions, and one should not make the mistake of “Nutpicking” by mistaking them for the majority views of the respective “other” side. This section is also not intended to offer a solution to this dispute, but merely to point out that the continuum fallacy contributes to driving both sides’ positions further apart than necessary – and making compromises seem more difficult than they need to be.

• 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