Är matematiken påhittad?

Jag har tidigare skrivit om fiktionalism inom etiken: att låtsas som om en objektiv moral finns trots att man är övertygad om att den inte finns. Det finns också fiktionalism inom matematiken:

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. … According to fictionalism, there is no mathematical knowledge apart from knowledge of the fiction of mathematics itself. Knowing that in the story of mathematics 2+3 = 5 is no more problematic than knowing that in the Tolkien story Bilbo Baggins is a hobbit. In both cases we know this by reading the relevant stories, listening to others who are well versed in the stories in question or, more adventurously, by exploring the logical consequences of the respective stories.

Grunden för matematisk fiktionalism är dessa tre överväganden:

There are several problems associated with admitting mathematical entities into one’s ontology. First, accepting mathematical entities would seem to run into trouble with Ockham’s razor. This is the advice not to multiply entities beyond necessity. It would appear that nominalists of all varieties have Ockham on their side, since they do not need to posit the huge number of entities entertained by Platonists. Second, mathematical entities are epistemically suspect. Mathematical entities are usually taken to be abstract, in the sense that they do not exist in space and time and do not have causal powers. It is thus mysterious how we can have knowledge of such causally isolated entities (Benacerraf 1983); or at least, an account is required of how the methods of mathematics are reliable means of forming beliefs about such abstract entities (Field 1989). Finally, we might add a more general worry about the metaphysical dubiety of abstract entities. After all, entities not located in space and time and without causal powers are utterly unlike any other entities we know about.

Det var inte riktigt vad jag fick lära mig i skolan när jag började räkna. Tur var nog det.