The phrase "accept this testimony" is correct and usable in written English.
It can be used in contexts where someone is requesting or urging another person to acknowledge or consider a statement or evidence provided.
Example: "In light of the new evidence presented, I urge the court to accept this testimony as valid and credible."
Alternatives: "acknowledge this statement" or "consider this evidence".
Sometimes religious courts do not fully accept the testimony of children or women, making proving molestation claims very difficult.
In addition, the Guardian saw police papers that show how quickly – within 36 hours – detectives appeared to believe and accept the testimony of taxi driver Zola Tongo, which was vital to the prosecution's case.
We wouldn't accept the cold war and the threat of MAD (mutually assured destruction) underpinning it; we wouldn't accept the Thatcherite attack on the unions and the consequent privatisation of public enterprises; and we wouldn't even accept the testimony of our senses when we saw the people surrounding us whipped into an acquisitive frenzy by the City's Big Bang.
Corresponding to the authority you ascribe and the trust you extend to the stranger, you impose a duty on yourself to accept the testimony, unless you have specific reason to object.
These discussions, and in less direct ways those for the Assurance View, pose a difficult question: How can, or how does, this vulnerability (to insincerity, specifically), dependence on good will, and empathy constitute part of the hearer's reason to accept the testimony of the speaker?
For example, in looking at a straight stick in water, even though it appears bent, we know from past sense experiences not to accept the testimony of our senses at face value in such situations because we have learned that straight sticks look bent in water.
In Hindu philosophy, yoga is the name of one of the six orthodox (which accept the testimony of Vedas) philosophical schools.
The reality, however, is that jurors typically accept the testimony of these reprobates, even though to believe such testimony would seem to defy common sense.
