Fallacy-fallacy

A 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.
Therefore: all tigers are cats.

This conclusion is invalid!
Therefore tigers are not cats.

The syllogism inserted in the top is fallacious, because of an undistributed middle term, i.e. it is clearly invalid - nevertheless, the result is true: Tigers actually do belong to the cat family.

• Argumentum ad logicam
• Argument from fallacy

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 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.

In principle, every fallacy-fallacy is based on a logical fallacy. Depending on it can be formulated, it might be one of the following:

Either as denying the antecedent:

If A is true, [then] B is true.
A is not true.
Therefore: B is not true.

Or as denying a conjunct:

It can not both be true, A and C.
A is not true.
Therefore: C is true.

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 (red herring).

One line of argumentation that one hears or reads in connection with the climate change debate could be paraphrased as follows:

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

Indeed, it follows from 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.

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 ice sheets. Those on Greenland and Antarctica are only the two most important and largest.

This form of argumentation has aspects of a 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 nutpicking.

• Argument from ignorance
• Denying the antecedent
• denying a conjunct

• Argument from fallacy on Wikipedia
• Argument from Fallacy on Logically Fallacious
• Fallacy fallacy on RationalWiki