The Mystery of Property F

March 10, 2024•339 words

A few years ago when I had first been introduced to philosophy, I was reading about illusions as an argument against naïve realism. The author presented the argument as a simple one: in illusions, someone perceives some object having some property 'F', although it does not "really" have this property. Therefore, that person must be perceiving the object indirectly.

The argument is a fairly convincing one, and certainly raises a big enough issue to make the naïve realist to reconsider their position, or at least adapt it to respond accordingly. To me though, this argument raised quite a different question: why F? At the time this was merely a passing thought; I simply assumed a random letter was chosen, and it happened to be F.

However, as I spent more time reading philosophy (particularly logic), I found that F is used quite frequently as a placeholder for predicates in logic. My curiosity was ignited, and it was furthered when a mentor recently referred to this mysterious 'property F', despite admitting that she did not quite know why she did so upon questioning. The other common ones seemed to have at least plausible explanations for their origins: a, b, and c would be used for fairly obvious reasons, and x, y, and z, were seemingly popularised by Descartes' use in La Géométrie [1]. But for F, it doesn't seem so clear.

Reading Mill's 'A System of Logic' [2], I found a potential answer. In Mill's context, F refers to 'a certain function of a given number'. This appears to be a plausible explanation, and one probably worth accepting for the time being - or at least, one of why F is used in logic.

But what about property F? Surely it would be absurd to suppose the author meant 'property function'. Perhaps philosophers simply saw instances such as Mill's and began to adopt F as a way to generally refer to unknowns. Of course, this remains merely speculation, and the mystery of property F remains unsolved...