All of it is subjective. It was considered moral to kill anyone who was not part of a tribe, and eat them, for many tribal cultures of the past. But today many, not all, societies now consider that unethical. History is riddled with such clear and solid evidence demonstrating how subjective things are.
We know our laws are subjective, yet like ethics, we define them based on what helps society as a whole function better, that's instinctual in itself as well. Empathy, a genetic trait by all accounts, plays a role in most mammalian species, and many others, in forming societies, it's one of our primary social traits. Some people lack this trait, and thus we tell them to just live by our rules or remove yourself from our society. Empathy varies too, it's not even a solid "yes" or "no," nothing about living organisms can ever be defined as dichotomies.
The reason this whole "objective morality" nonsense started was as a method of controlling the masses without government, fear tends to be a very effective method in getting people to do what you want them to do. What stops psychotic people from killing? The threat of losing their freedom, there are many psychotic personalities living in even the most civilized societies, freely contributing like all other members, and finding other ways that will not risk the loss of freedom to sate this urge to hurt something, video games are one really good method.
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There are quite some truths we accept without "evidence" (a priori truths). Examples are: laws of logic, truths of mathematics, introspective beliefs, human perception of the external reality in general, memory beliefs, and so on.
David Hume in his Inquiries Concerning Human Understanding argued that science is a non-rational enterprise, because the premise of science- induction- cannot be substantiated with evidence. His problem was, he didn't acknowledge the existence of a prior beliefs, things we simply know to be true without having evidence to believe them. These are integral parts of human noetic structure.
Yeah ... nope. Everything that we accept as fact is supported by evidence, anything that is not supported by evidence is delegated to guess.
Oh wait, you were talking about "truths" ... as far as I can see no one has lied. You should be careful of your wording, really. Using the word "truth" in that manner is highly inaccurate, science doesn't dictate reality, unlike what religion attempts to do, and thus we deal with facts, evidence, and results, everything else is generally useless after exploration into a matter has begun. We do understand how memory works, that's just too easy, neurologists are pretty certain how it works and we even design AIs that simulate this pretty well, just not the "laws of logic," that you brought up.
Laws of logic can be demonstrated, and the demonstration is supporting evidence. Belief is just superstition, actually a genetic instinct to fear the places we cannot immediately comprehend, thus we create stories about what's in the shadows ... but it's all made up. It's why kids often insist there is a monster under the bed, it's that same instinctual trait that kept our ancestors safe when they first climbed from the trees.
Perception is another easy one, it's demonstrated all the time to every living person. Hate to burst your bubble, but there is no "sixth sense" of any sort, there is no "knowing something is true without evidence." Every fact can be demonstrated to work the same in all cases, at all times, if such a demonstration cannot be made, then it's not a fact.
