Jamesian Philosophy Refreshed

  Now that those of us with a lively but an amateur interest in cosmology have sort-of gotten our heads around the idea of a black hole, we have to wrestle with an odd variant, the "naked black hole" -- i.e the black hole that can be observed from outside. We amateurs understand or think we understand that the inner workings of a black hole cannot be observed from outside its boundary, formally known as its "event horizon". Hence the adjective "black". Yet the James Webb telescope seems now to be saying -- yes, maybe we can. Perhaps sometimes we can observe the singularity, the point at the Senate where gravity becomes infinite and all laws seem to break down.  Here is one take on this. https://backreaction.blogspot.com/2025/09/this-naked-black-hole-shouldnt-exist.html One thing that us amateurs think we know about black holes is that they form from the collapse of a star in upon itself.  Hossenfelder says that the naked black holes did not form that way, ...

Recently, the physicist Sabine Hossenfelder, who maintains a wonderful blog, posted her thoughts about "infinity," its necessity as a mathematicians' tool, on the one hand, but its unreality from the point of view of the science of physics, on the other. Her point is that a physicist only regards something as real if it is necessary in order to explain an observation. Infinity, she says, will never fill that bill.   She also went a bit into the mathematics of infinity, and the fact that not all infinities are the same. The real numbers are a different sort of infinity from the integers. I used the co mment section under her blog post to ask a question that has long been on my mind.  I remember when I was a kid, many decades ago, some of us nerdy types excitedly read "One, Two, Three, Infinity" by George Gamow. Gamow covered some of the same territory you just did although I'm guessing progress has been made in the last half century or so. If I recall corr...