I don't think logical proofs work for this kind of topic. Surely in philosophy, it's great to have analytic definitions. (Though I'm not sure you've generated great analytic definitions.) But treating concepts such as "goodness" and "badness" as variables in a logical proof just doesn't seem to make much sense.
But the real problem with this entire attempt is that there is a glaring ambiguity. The word "exists" can be understood in two different ways, and you seem to play on this. In your title, you seem to treat "exists" ontologically: that is, as to whether or not there is an objective status for goodness as a real feature of the world around us. Yet here, where you say "then all things are equally preferable", you seem to treat "exists" subjectively - (as an intersubjective quality of human experience).
Here is the logical flaw in doing so. By confusing these two very different meanings of "exists", you run into this problem: that it is possible for there to be no objective goodness (as an ontological feature of the world) and yet for goodness to exist in degrees (subjectively), such that it would not follow that "all actions are equally preferable" (or, more simply, that relativism
is true). Goodness would not exist objectively, but would exist in degrees subjectively (relative to human experience, or the human condition). And so, if goodness existed subjectively at least, we'd have reason to say "not all things are permissible". And even if goodness did exist as a separate and distinct ontological feature of reality, it wouldn't necessarily follow that goodness exists in degrees in human experience (subjectively). This is because even if goodness was objectively real, we may not know it, in which case "all things would be permissible/preferable". For goodness as a feature of subjective human experience is contingent. That is, it could have been the case that humans never experienced or understood the quality of goodness
So, this sounds like a kind of equivocation
. Clever sophistry, but bad logic.
Secondly, you commit a kind of categorical error
in conflating moral permissibility
(as someone suggested). And certainly, it's easy to see why. Both morality and truth are thought to be either absolute
. (And further, moral absolutism
is confused with the ontological status of morality
in your argument. But these are two different things. Moral absolutism has to do with whether or not moral truths hold the same for everyone, or if there are no more truths and only relative moral values. And the ontological status of morality clearly has to do with to what extent morality is either an objective feature of the world, or merely a subjective result of human valuation.) So you are essentially saying "morality is either real or it is relative", but this extremely illogical and mistaken. You cross ontology with axiology. But these are two very distinct philosophical sub-disciplines. (One deals with reality, while the other deals with values. And denying one does not imply the other, necessarily, and vice versa.)
But moral permissibility and truth have nothing to do with one another, just as ontology and axiology are logically distinct philosophical matters. If nothing is ever morally impermissible, it doesn't follow that "all things are true". It follows that "all actions are morally permissible". And so, it wouldn't follow from moral relativism that it is true that moral goodness exists (in either sense of the word "exists"). Because again, the idea that all actions are permissible does not mean that all statements are true.
Truth and morality are distinct conceptual topics. To confuse them with one another is a kind of category error. (That is, you do not treat a state of morality as if it holds implications for truth - especially about some other state of morality.)
There may have been other fallacious errors, but this is all I could easily pick out.
Enjoy your day.
(Graded for a philosophy professor, tutored for logic, and helped students review for professional ethics - as an SI Leader. I also impressed many of my professors with some of my work. So you could say this is natural for me.)