All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today.

All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today.

It may seem rash indeed to draw conclusions valid for the whole universe from what we can see from the small corner to which we are confined. Who knows that the whole visible universe is not like a drop of water at the surface of the earth? Inhabitants of that drop of water, as small relative to it as we are relative to the Milky Way, could not possibly imagine that beside the drop of water there might be a piece of iron or a living tissue, in which the properties of matter are entirely different.

Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.

The occurrence of any event where the chances are beyond one in ten followed by 50 zeros is an event which we can state with certainty will never happen, no matter how much time is allotted and no matter how many conceivable opportunities could exist for the event to take place.