Recent developments in the philosophy of logic suggest that the correct foundational logic is like God in that both are maximally infinite and only partially graspable by finite beings. This opens the door to a new argument for the existence of God, exploiting the link between God and logic through the intermediary of the Logos. This article explores the argument from the nature of God to the nature of logic, and sketches the converse argument from the nature of logic to the existence of God.

It was my nine-year-old daughter who got me interested in the title question. As she appreciates, multiplying an integer by a power of 10 is a cinch. To multiply 34 by 100, simply add two zeros at the end: 34 × 100 = 3400. Dividing 3400 by 100 is the reverse process: remove two zeros to obtain 34. More generally, to multiply an integer by 10N, for non-negative N, add N zeros to the end of its decimal notation, and to divide an integer by 10N remove N zeros from its end — so long as it has them. Easy-peasy; my daughter knows all that.

Metamathematics is the mathematical study of mathematics itself. Two of its most famous theorems were proved by Kurt Gödel in 1931. In a simplified form, Gödel's first incompleteness theorem states that no reasonable mathematical system can prove all the truths of mathematics. Gödel's second incompleteness theorem (also simplified) in turn states that no reasonable mathematical system can prove its own consistency. Another famous undecidability theorem is that the Continuum Hypothesis is neither provable nor refutable in standard set theory. Many of us logicians were first attracted to the field as students because we had heard something of these results. All research mathematicians know something of them too, and have at least a rough sense of why ‘we can't prove everything we want to prove’.

Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness (proportionality and shortfall minimization) before offering a formal proof that no non-trivial theory guarantees aggregativity. This is not intended as a criticism of any particular theory, but as a datum that must be taken into account in constructing a theory of fairness.

Without doing the morally unspeakable or the medically infeasible, can a preference for daughters rather than sons increase their relative number? If, to be more precise, the only variable over which you have control is your number of children, can you increase the ratio.

Expected value (no. of daughters) : Expected value (no. of sons) ? Naïvely, you might think so. If for example you adopt the policy ‘stop procreating as soon as a girl is born’ won't you bear more girls compared to boys than you would otherwise? No, in fact.