persuade through reasoning

The method to be used in debates is to present the facts, reason things out, and persuade through reasoning.

辩论的时候，必须采取摆事实，讲道理，以理服人的方法。

《新英汉大辞典》

Likewise, through extensive reasoning, one might persuade someone that eating meat is wrong; but the only arguments that will work are ones that appeal to prior sentiments.

同样，通过广泛的推理，一个人可以说服吃肉的人，让他明白吃肉是错误的，但如前所述，只有吃肉的人对偏执行为持否定态度，推理才会对他有效。