Banking and semantics

I have a job at a bank. On a bad day it seems to make little sense (other than in pounds and pence). On a good day there is enough sophisticated semantics to pass round, straightforward as it might look at first sight.

Why straightforward? Because banking is about balance sheets. Balance sheets are about numbers. Numbers are mathematics. Mathematics is extensional and does not allow intensional paradoxes.
So banking does not allow intensional paradoxes.

But this reasoning is certainly untrue.

(if you do not know what intensional contexts are click here to see previous entry)


Banking’s basic equation, sort of E = mc2 , is

(1)TOTAL ASSETS = TOTAL LIABILITIES

Hence,

(2) ASSETS = LIABILITIES

Now let us take the assumption which all the bankers recognise as true

(3) DEPOSITS ARE LIABILITIES

Next, from (2) and (3) you can derive by substitution

(4) DEPOSITS ARE ASSETS

which is false, absurd even (because deposits are on the liabilities side of the balance sheet).

The bottom line is that when we talk about the balance sheet the Fregean, compositional semantics does not work, because the talking of assets and liabilities involves intensional contexts. Now, this is puzzling, because it would seem that the balance sheet is pure mathematics, which is extensional.