No, that is the great fallacy; the wisdom of old men. They do not grow wise. They grow careful.
The remark challenges the common assumption that age naturally produces wisdom. Instead, it suggests that older people may appear wiser because experience has made them more cautious. Having encountered danger, failure or disappointment, they may become more reluctant to take risks, and that restraint can be mistaken for deeper understanding.
In A Farewell to Arms, the distinction between wisdom and carefulness fits a world shaped by uncertainty, violence and loss. Experience teaches people how easily plans can fail and how vulnerable they are to circumstances beyond their control. The line does not necessarily dismiss the value of caution; rather, it questions whether caution should automatically be treated as wisdom. Its broader point is that age changes behaviour as well as judgement, and the two should not be confused. Someone may avoid mistakes because they understand more, but they may also simply have become more aware of the possible consequences.