"undermine this problem" is correct and usable in written English.
You can use it when you want to express or suggest that someone or something is causing a problem to become worse or to be weakened. For example: "The government's budget cuts have undermined this problem and hindered progress on the issue."
It seems equally natural, however, to respond to Laudan and Leplin simply by conceding the variability in empirical equivalence but insisting that this is not enough to undermine the problem.
But there are many ways to achieve balance, such as debating the different ways to tackle a problem, which don't have to involve undermining the problem itself.
The batting problems which have undermined this campaign - Scotland have been bowled out in all but one game - were evident again as five players made ducks.
This fault-finding approach may demoralize health workers and undermine joint problem-solving and action, so health programmers and providers favor forms of supervision that focus on addressing problems in service delivery [ 5, 7, 8].
As I can testify from experience as a senior economist at the bank, this problem undermines the organisation's anti-corruption efforts.
This problem undermines confidence in the technology[ 1] or, potentially worse, may misdirect the researchers into suspecting strange biological processes.
This problem has undermined public confidence in the mental health system and caused a strong dissatisfaction among consumers and carers [ 8, 11].
As the validity of a meta-analysis where the fading of reported effectiveness is present may be undermined, we propose to consider this problem in future meta-analyses.
There Stroud contends that such transcendental arguments are undermined by a problem which can be stated quite generally.
And he said the country's ability to lead and inspire around the globe was being undermined by problems at home.
