(Deleted my comment since I realized that it can be both an empty set and None.)

Seems like this breaks several other things.

I'm not sure which fix is better, or if there is any other superior solution available. Based on the commit history, there are two potential fixes:

1. alternative fix. The fix produces the expected outcomeand aligns with the description in the doc:

If labelOnlyBase is False, these two numbers control the labeling of ticks that are not at integer powers of base; normally these are the minor ticks. The controlling parameter is the log of the axis data range. In the typical case where base is 10 it is the number of decades spanned by the axis, so we can call it 'numdec'. If numdec <= all, all minor ticks will be labeled. If all < numdec <= subset, then only a subset of minor ticks will be labeled, so as to avoid crowding. If numdec > subset then no minor ticks will be labeled.
...
To disable labeling of minor ticks when 'labelOnlyBase' is False, use minor_thresholds=(0, 0). This is the default for the "classic" style.

Note that it assumes labelOnlyBase is True for all the major formatters while False for minor formatters, which could contradict with the doc stating:

This is normally True for major ticks and False for minor ticks.

What about "abnormally"? Can a major formatter have 'labelOnlyBase' set to False? Is there an exceptional case?

2. FIX: LogFormatter minor ticks with minor_thresholds of (0,0) misbehaves. It uses the same minor_thresholds logic for both major and minor formatter, and allows a major formatter with labelOnlyBase=False or a minor formatter with labelOnlyBase=True. But it contradicts with the following description in the documentation:

If labelOnlyBase is False, these two numbers control the labeling of ticks that are not at integer powers of base; normally these are the minor ticks. The controlling parameter is the log of the axis data range. In the typical case where base is 10 it is the number of decades spanned by the axis, so we can call it 'numdec'. If numdec <= all, all minor ticks will be labeled. If all < numdec <= subset, then only a subset of minor ticks will be labeled, so as to avoid crowding. If numdec > subset then no minor ticks will be labeled.

When minor_thresholds is set to (0, 0), namely, numdec > subset, a formatter labels bases only whether labelOnlyBase is True or not. In the example from issue #25896, its outcome is as follows:

import matplotlib.pyplot as plt
import matplotlib.ticker as mticker

fig, ax = plt.subplots()
ax.set_yscale("log")

formatter = mticker.LogFormatter(minor_thresholds=(0,0))
ax.yaxis.set_minor_formatter(formatter)

ax.set_ylim(10, 20)

formatter(10) # '10'
formatter(11) # ''
formatter(12) # ''
formatter(13) # ''
formatter(14) # ''
formatter(15) # ''
formatter(16) # ''

Furthermore, what does the term "classic" style refer to in the documentation? Maybe we could provide a more precise description.

Classic is the pre-2.0 default style.

Hi @oscargus, could you review the PR again?