It is important not to confuse the question of the fallibility of our cognitive faculties, including reason in us, with the question whether there is truth. A fallibilist is not a truth-denier. One can be -- it is logically consistent to be -- both a fallibilist and an upholder of (objective) truth. What's more, one ought to be both a fallibilist about some (not all) classes of propositions, and an upholder of the existence of (objective) truth. Indeed, if one is a fallibilist, one who admits that we sometimes go wrong in matters of knowledge and belief, then then one must also admit that we sometimes go right, which is to say that fallibilism presupposes the objectivity of truth.
Just as a fallibilist is not a truth-denier, a truth-affirmer is not an infallibilist or 'dogmatist' in one sense of this word. To maintain that there is objective truth is not to maintain that one is in possession of it. One of the sources of the view that truth is subjective or relative is aversion to dogmatic people and dogmatic claims.
But if you reject the objectivity of truth on the basis of an aversion to dogmatic people and claims, then you are not thinking clearly.
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