The NAXALT Argument as Distraction Premise

715 words

The NAXALT argument is based not on a false premise but a misleading one which is intended to distract from, and pose as, the main premise. It is reducible to logical form, but with the proviso that this is analogous, and the whole problem is partly rhetorical. Analogously, then, the NAXALT argument is well illustrated by a mathematical conundrum.

Three men move into an apartment and wish to buy a television. They see a second-hand set in a shop window for £30 and, each having £10, they decide to club together and buy it. The shop assistant is happy to sell it to them subject to his boss’s approval. He takes the £30 and goes into the back of the store to see the boss, who tells him that he can sell the TV to the men. However, he, the boss, has made a mistake with the pricing, and the TV should actually be marked up at £25. The assistant sees a chance to make a little extra money for himself, and goes back into the store to tell the men that they can buy the TV, but that the price is actually £27. As the men have each given him a £10 note, he gives them each £1, leaving them happily having paid £27 in total. This leaves the assistant with £2 for himself. 27 (what the men have paid) plus 2 (what the assistant has pocketed) equals 29. What has happened to the missing pound from the original £30?

The answer, of course, is that nothing has happened to it as there is no missing pound. The story has been constructed to persuade the listener of the false premise that the price of the TV is what the men paid for it, £27. This is not, however, the price, which is £25. £25 plus the £3 returned to the men plus the £2 the assistant keeps equals £30. The price was never £30 or £27. These are distracting premises providing the illusion of a missing pound. The price of £25 is the actual premise.

Transposing this misleading construction to the NAXALT problem, we find that the distracting premise is the fact that “not all X’s are like that”. “Like that” can be restated as “what is the case”, and so takes standard logical form as p. Thus, “not all X’s are like that” has as its logical form “not all x is p”, which looks like it is the major premise when used rhetorically by the proponent of the NAXALT argument. But this is not the major premise, which is rather “some x is p”. Using as an example the Manchester Arena bombing, carried out in 2017 by a devotee of Islam and which killed 22 and injured 1,017. In this case, “not all x is p”, or “not all Muslims are terrorists”, is not the major premise, because that undeniable fact did not produce the explosion, which in turn produces the argument. The major premise which supports the facticity of the explosion is “some x is p”, whereas the NAXALT argument privileges “not all x is p”. Analogously, “not all x is p” has taken the place of the two false prices in the story of the TV set. It is a distraction from the major premise and leads to an illusory outcome.

A subsidiary consideration is the selective use of the NAXALT argument. We are used to hearing that “not all Muslims are terrorists”, and the statement is true within the relevance of its function. However, if the subject is rape, and the disproportionate number of such assaults carried out by non-whites, the focus suddenly changes to “all rapists are men”. “Men” therefore become the problem, rather than the prevalence of certain ethnicities in incidences of rape. The NAXALT argument is momentarily and expediently replaced by the AXALT argument. This is illegitimate in logical terms as “not all x is p” is selectively replaced with “all x is p” to suit political expediency and cannot therefore function as a rule. Without incontrovertible rules, you can’t have logic.

In summary, NAXALT is based not on a false premise, but a falsely misleading one, “not all x is p”, which is intended to distract from the central premise in which “some x is p”. Without a central premise, operating in its centrality and not as a deposed subsidiary to the argument, there is no argument to begin with.