====== Fallacy-fallacy ======

A [[relevancy:index|fallacy of relevancy]], whereby a refuted argument is (mistakenly) taken as evidence for the contrary proposition.

For example:

>> All //cats// are //animals//.
>> All //tigers// are //animals//.
>> <s invalid conclusio "Illicit process">Therefore: all <em>tigers</em> are <em>cats</em>.</s>
> This conclusion is invalid!
> <s invalid conclusio "Fallacy-Fallacy">Therefore <em>tigers</em> are not <em>cats</em>.</s>

The [[glossary:syllogism|syllogism]] inserted in the top is fallacious, because of an [[logic:formal_fallacies:fallacies_of_distribution:undistributed_middle|undistributed middle term]], i.e. it is clearly invalid - nevertheless, the result is true: [[wp>Tiger|Tigers]] actually do belong to the [[wp>Felidae|cat family]].

===== Other names =====

  * <span "Lat: argument from (misunderstood) logic"><i :la>Argumentum ad logicam</i></span>
  * Argument from fallacy

===== Description =====

A refuted argument becomes //invalid// as evidence for the position it claims to hold. However, it does not automatically follow that the position is //wrong//. For this, all other arguments pro and contra must first be assessed.

The //fallacy-fallacy// has some similarity with the [[rhetorics:defasible_arguments:argument_from_ignorance:index|argument from ignorance]] in that it is based on the //absence// of evidence. However, in this case a refuted argument is reinterpreted as an argument for its counterposition, whereas in the other case the absence of evidence is interpreted as evidence of absence.

==== Logical fallacy ====

In principle, every //fallacy-fallacy// is based on a [[logic:index|logical]] fallacy. Depending on it can be formulated, it might be one of the following:

Either as [[logic:formal_fallacies:denying_the_antecedent|denying the antecedent]]:

> //If// A is true, [//then//] B is true.
> A is //not// true.
> <s invalid conclusio "denying the antecedent">Therefore: B is //not// true.</s>

Or as [[logic:formal_fallacies:denying_a_conjunct|denying a conjunct]]:

> It can //not both// be true, A //and// C.
> A is //not// true.
> <s invalid conclusio "denying a conjunct">Therefore: C is //true//.</s>

===== Examples =====

This form of fallacious argument is commonly used in discussions and is often in a subtle and rather implicit way in order to distract from stronger counter-arguments (<span maniculus "see:">[[rhetoric:red_herrings:index|red herring]]</span>).

==== Melting icebergs and rising sea levels ====

One line of argumentation that one hears or reads in connection with the [[wp>Global warming controversy|climate change debate]] could be paraphrased as follows:

> A: <u questionable "questionable statement">When icebergs melt [as a result of climate change], the sea level will rise by many metres, whole coastal regions will be submerged.</u>
> B: When icebergs [that float in water] melt, the melt water takes up just as much space as the floating iceberg did before. <s invalid fallacy-fallacy">The fear of rising water levels due to climate change is therefore unfounded.</s>

Indeed, it follows from [[wp>Archimedes' principle|Archimedes’ principle]] that a floating body displaces as much water as corresponds to the weight of the body. A (floating) iceberg that melts therefore does not (or only marginally) contribute to a rise in sea level.

<aside info>
**Note:** As is often the case, the matter is actually a bit more complex: there are differences in the thermal expansion of water, in the behaviour of salt water versus fresh water, and in how much energy is reflected from white bodies (ice/snow!). But these are all rather less relevant in this context.
</aside>

However, this does not mean that global warming would not have an impact on sea levels: in addition to the floating icebergs, there are also enormous amounts of inland [[wp>Ice sheet|ice sheets]]. Those on [[wp>Greenland ice sheet|Greenland]] and [[wp>Antarctic ice sheet|Antarctica]] are only the two most important and largest.

This form of argumentation has aspects of a [[rhetoric:defeasible_arguments:strawman:index|straw man argument]], as it distracts from the actual argument in order to try to refute a much weaker one. If one would even deliberately single out somebody who represents this weak position in order to present this as "typical" for the counter side, this would even count as a form of [[rhetorics:red_herrings:ad_hominem:guilt_by_association:nutpicking|nutpicking]].

===== See also =====
 
  * [[rhetorics:defasible_arguments:argument_from_ignorance:index|Argument from ignorance]]
  * [[logic:formal_fallacies:denying_the_antecedent|Denying the antecedent]]
  * [[logic:formal_fallacies:denying_a_conjunct|denying a conjunct]]

===== More information =====

  * [[wp>Argument from fallacy]] on //Wikipedia//
  * [[https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/51/Argument-from-Fallacy|Argument from Fallacy]] on //Logically Fallacious//
  * [[https://rationalwiki.org/wiki/Fallacy_fallacy|Fallacy fallacy]] on //RationalWiki//