Ideas can be proven true or false, but only in the context of other ideas which are assumed. That is what all of mathematics is based on. Of course, there is no objective truth or falsehood - the world doesn't even exist in a single objective state - and inductive inference is merely sufficient to provide estimates of probability.
Core values can't be falsified, but a belief system built atop these values can be shown to be inconsistent, meaning it can essentially be used to argue for anything. Like in mathematics, an ideal system would pick core axioms/values that don't lead to inconsistency.
> Nothing is purely true or false because everything falls on a continuum.
That statement sure isn't purely true. (Therefore, there must at least kind of be something which is either purely true or purely false.) Though perhaps the sentiment behind it might not be totally wrong?
This is not correct. There is no such thing as absolute truth. Something can only be true within a set of previously agreed constraints and rules. For example, I can simply imagine a scenario where a=0 implies a=0 is considered to be false, because I define it to be so.
Given the subjective nature of the statement I do not find it particularly disturbing to consider it may not be objectively true. Additionally, I disagree with the implication that because a conclusion is not reached through logic it is not objectively true. For one, there may still exist a logical argument whether I have made that argument or not. For another there is no guarantee that logic leads always to truth or that truth can only be found with logic. (Although I do find those two ideas rather disturbing...)
The fun thing about facts is that nobody needs to decide whether or not they are true. Perhaps the fact that you can honestly claim to think otherwise means you need to take a step back and examine your reasoning.
"In order for discussion to have any meaning, the things we claim have to be 'falsifiable'; there has to be SOME observable consequence of a claim being either true or false, even if we aren't able to currently observe it."
> If everything that one person chooses to believe is true for them, and that person chooses to believe that there is an objective truth that precludes this statement, then you have a problem.
I can't parse this sentence at all -- mostly, I think, because "true for them" doesn't seem to mean anything. Can you clarify? Also, what's the problem you're talking about?
Actual reality and Truth are the same thing. Because two parties cannot agree on what they perceive the Truth to be does not imply it doesn't exist. In fact, both parties could be wrong - Truth could be a 3rd thing both are oblivious to.
In that case the statement "if $assumptions, then $conclusion" is objectively true.
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