It's very hard to entertain the statement: "There is no objective purpose in the world" as true, because the statement is self contradictory.
Which part of the statement is objectively true? The part which denies objective purpose, or the part which affirms it?
This is why earlier I mentioned that without objective value, nothing makes sense.
Descriptions of the world don't make sense.
Judgements don't make sense.
Actions don't make sense.
Statements of any kind don't make sense.
You're probably wondering which part of the statement I think "affirms" objective value, so here it is:
First off, the statement is an action, and therefore it is inherently an expression of value (even according to subjective value theory).
In order to generate that statement, (let's call it a description of the world), you had to value certain perceptions, concepts, thoughts, ideas, words, the English language itself, over others. These values are baked into the truth-value of the statement.
The truth-value of a statement depends partially on the context-dependant objective value of the means by which the statement was generated and conveyed.
Moreover, you're attempting to adhere to a logical framework that under subjective value theory only exists subjectively, not objectively. This is because logic itself is a framework of value.
I want to be able to assume the premise is true, then explain my reasoning from there, but because they premise is self contradictory, anything following will be incoherent.