As others have mentioned, an epistemic inability/failure doesn't imply an ontological impossibility.
However, as I have dared raised this elsewhere, there's actually a very prolific line of research spanning over a century showing that mind can influence physical/biological bodies in dramatic or noticeable ways. The generic phenomenon is known as psychokinesis or distance mental influence, and comes in many varieties depending on whether the target is a living thing or not, human or not, the kind of influence and circumstances.
For unfortunate reasons, this kind of research which has produced good-quality replicated results has been totally ignored or dismissed by modern academia and has been thus absent from the philosophy of mind debate, despite their huge implications.
A review by William Braud of bio-psychokinesis research can be read here. He cites controlled and responsible experiments producing positive results. And here's description of a typical experiment:
In a typical experiment of the type to be discussed, one selects a
living organism and isolates it, usually at a distance, from all
conventional sensori- motor or energetic influences of the
"influencer." In principle, any living organism may serve as this
"target." Next, one selects some readily measured aspect of the target
organism's activity, objectively monitors that activity over a period
of time, and generates a permanent record of that activity. It is,
perhaps, desirable to choose an activity which occurs with moderate
frequency or intensity and which is relatively stable over time,
although this is not an essential requirement. An "influencer" then
attempts to influence the organism's activity, mentally and at a
distance, in a prescribed fashion and according to a predetermined
(and, ideally, random) schedule. Conventional statistical
methods are used to compare the organism's activity during periods of
attempted mental influence with activity levels during comparable
non-influence, control periods.
Edward Kelly et al. in their more general review of various kinds of PK research, among other examples, cite experiments involving an influencer attempting to arouse a target with the target's response measured by reactions of the nervous system. They cite controls and results:
Experimental methods have been designed specifically to rule out
conventional explanations for any response seen in the target persons,
such as suggestion or expectation, sensory cues, naturally occurring
internal rhythms in the autonomic nervous system, recording errors,
arbitrary selection of data, and chance. For example, the two persons
are isolated in separate rooms with no sensory contact possible,
experimental and control periods are randomly interspersed in an order
that is automatically generated, and responses are recorded
automatically. Under these general conditions, the results over
numerous studies have been reasonably consistent and robust. In an
overview of 19 studies conducted at three labs, Schlitz and Braud
(1997) found an overall success rate of 37%, when 5% would be expected
by chance (p = .0000007, effect size
= .25). In a more recent and conservative meta-analysis of 37 studies, S. Schmidt et al. (2004) found a somewhat smaller, but still
significant effect (p
= .001 , effect size = .11) (Irreducible Mind, 230-231)
Irreducible Mind is a massive work which catalogues multiple categories of evidence from psychical research that falsify physicalism and support dualism, mental causation and survival of consciousness after bodily death. Yep, a highly ambitious, daring and controversial thesis among the modern scientific establishment but carried out meticulously and with critical scientific spirit throughout which has so far met no physicalist rebuttal and mostly disregard.