I'm trying to make sense of Beyond Good and Evil and Nietzsche's views at that time.
The claims he makes about truth and logic seem problematic to me:
"Granted, we will truth: why not untruth instead?" - page 5
It seems that, although Nietzsche may concede to the existence of absolute truth, he takes issue with human tendency to value it above all other things.
"We do not consider the falsity of a judgement as itself an objection to a judgment ... The question is how far the judgement promotes and preserves life" - page 7
Nietzsche seems to submit alternative metrics for determining the value of knowledge, which allow perspectives to attain a level of value greater than or equal to that of absolute knowledge. I've heard people say that he didn't believe in absolute truth or falsity at all. However, here he seems to acknowledge the existence of absolute truth, while arguing about its value.
"And we are fundamentally inclined to claim that the falsest judgments (which include synthetic judgments a priori) are the most indispensable to us, and that without accepting the fictions of logic, without measuring reality against the wholly invented world of the unconditioned and self-identical, without a constant falsification of the world through numbers, people could not life" - page 7
In this quote, I'm assuming that Nietzsche refers to objective reality with the word "reality," rather than perspective reality? Nietzsche makes a dig at the idea that the world can be perfectly described by mathematical models, which is quite reasonable. However, he also seems to denounce the idea that there is an objective reality which is bound to consistency with the rules of formal logic. Of course, much of logic is necessarily valid because of how it is defined, and cannot possibly be disputed. A rock cannot be both hard and not hard at the same time (law: x != (!x)). The statement "It is raining or it is not raining" is irrefutably true (law: x || (!x) == true). Nietzsche must not be disputing the validity of these laws, but instead synthetic a priori laws. I would guess that he is asserting that we should not quibble about whether or not our perspectives are logically sound at the finest level, because it is more important that those perspectives be life-affirming.
"synthetic judgments a priori do not have to be possible at all: we have no right to them, and in our mouths they are nothing but false judgments." - page 13
The way I understand them, synthetic a priori judgments are basically just truths which are not obvious by definition, but which can be proven with rigorous logic. Britannica states that "the truth or falsity of synthetic statements is proved only by whether or not they conform to the way the world is and not by virtue of the meaning of the words they contain." It seems that Nietzsche asserts that, since we cannot know "the way the world is" beyond our language-constrained perspectives, we cannot differentiate between synthetic and analytic a priori propositions.
In these sections, Nietzsche seems to denounce both truth and logic. This seems problematic since without basic logic, one cannot interact with the world in any meaningful way. Is his rejection really of logic's ability to lead us to truth? Is his goal just to raise healthy skepticism?
Did he actually have a firm (one might say "absolute") opinion on the un-absolutism of reality/logic, or did he just decide that we could never see around our perspective lens, so we should find something better to value?
P.S. If Nietzsche rejects truth and logic literally, how could we even make sense of such a world (where contradictions are possible)?