The phrase “falsehood is so near to truth that a wise man would do well not to trust himself on the narrow edge” is a quotation attributed all over the internet to the Roman philosopher Cicero, although rarely is a precise source for the quotation cited.
A source is cited in Hoyt’s New Cyclopedia of Practical Quotations (1922), as follows:
Ita enim finitima sunt falsa veris ut in praecipitem locum non debeat se sapiens committere. So near is falsehood to truth that a wise man would do well not to trust himself on the narrow edge. Cicero — Academici. IV. 21.
Horace Rackham’s translation of the larger passage (in the Loeb Classical Library) is as follows:
since it is agreed that to give assent to anything that is either false or unknown is so serious a fault, preferably all assent is to be withheld, to avoid having a serious fall if one goes forward rashly; for things false be so close to things true, and things that cannot be perceived to things that can (assuming there are such things, which we shall see soon), that it is the duty of the wise man not to trust himself to such a steep slope.
What does all this mean? It means, basically, that sometimes it is so difficult to distinguish truth from falsehood that it is best for a wise person not to claim that he knows either what is true or what is false. In other words, this phrase is an endorsement of skepticism and open-mindedness. It is a caution against intellectual pride and presumption. If a person doesn’t know for sure what is true and what is false (because the two are often hard to separate), that person should not claim to know the difference.