The formula of equation need not be applied to any specific thing when we are saying "2 + 2 = 4", but at the same time it is applicable to anything equatable. Unapplied, the formula has the significance that two things plus to more things equals four things. If we are looking to evaluate the truth of a unique thing (apple) to a different unique thing (orange), the formula cannot be used. John plus Joe does not equal John or Joe, or Bill for that matter. Unique identities are not equatable.PureX said:A mathematical formula has no context but itself until it's been applied to something actual. Even if a mathematical equation were an absolute truth, what significance would it have if it remains un-applied? And as you are admitting, yourself, the moment we try to apply it, it becomes only relatively true.
The moment we apply the formula has nothing to do with truth or relativity: the things we apply the equation to already exist, so they also already existed in relation to other things before we brought the formula in. What we are determining with our formula is the truth of equation.
What I hear you saying is that nothing with a unique identity is equatable, only things that share some bit of identity with other things can be equatable. Two unique things (actual things) equatable would be "the same thing"; an impossibility. I agree.PureX said:But there are no absolutely equatable things. Two absolutely equatable things would be the same thing. It's self contradictory. There are only relatively equatable things.
It is only self-contradictory if we expect that the actual things be equatable, but there is nothing in the rules of mathematics that says unequatable things have to equate and still be true.
Even those things with unique identity exist in relation to other things --in fact, they are defined only in relation to everything. That is how they can have an identity unique amongst everything else. This does not make them "relatively true", it makes them "truly relative".
I agree, equatability is dependent upon what 'criteria' we evaluate, in that we must necessarily be able to evaluate the same criteria on both sides of the equation; otherwise, no equation is possible. Nothing is equatable if we look only at the unique identities of things. The equation can only resolve as true or false if we look only at things in terms of shared characteristics and traits, things that are equatable.PureX said:Nothing is equatable, or everything is equatable, depending on how specifically we "identify" the things in question. The point is that the truthfulness of the equation depends upon some degree of lack of specificity of the identity of the things being equated.
This is where I fall down. This is saying a different thing than we just said above, an entirely different thing. Oh, it sounds the same, but it's not. Here you are saying that the truthfulness of equation is dependent upon how we look at it. You are implying that truth is dependent upon us.PureX said:That means that any mathematical equasion's truthfulness is dependent upon (relative to) the degree of vagueness of the identity of the things being equated. A relatively true mathematical equation cannot be absolutely true, as the concepts of relative and absolute are opposites.
The opposition of 'absolute' and 'relative' is unique to a particular context: namely perspective, or how we look at it. We cannot look at a thing both ways at once and still make sense, but we can look at it either way. We can look at a thing either absolutely, as a thing with unique identity, or relatively (in this example by looking to shared characteristics or traits). The actual thing doesn't change, just the way we look at it. In other words, something cannot be absolute and relative in the same context; but if we take into account the different contexts, the same thing can be absolute in one context and relative in another. The thing itself can be (and is) both absolute and relative. All that changes is the context.
Most everything is both absolute and relative, depending on context. Truth is special. Truth is always absolute, because there is only one context in which something is "true", that is the objective context. For the formula of equation, that is when equatable conditions are met and the formula balances. If the equation is true (meaning if we plug in equatable things), it is absolutely true regardless of what we chose to look at (that means, regardless of the relativity of the things involved to the actual thing or to each other). Two sheep plus two sheep equals four sheep. It really does. Two black sheep plus two black sheep equals four black sheep.
The truth of the equation is not dependent upon us and our subjective perspective.
I think what I meant by "out of context" was taking 'the equation evaluated is absolutely true' and turning it into 'the relative things equated make the equation only relatively true'. Only the first is actually a statement about truth.PureX said:But what you're calling "out of context", I'm calling actual application. My point is that the proposition can't really be true until it's been applied to something real.
There are no actual phenomena that are absolutely equitable, so as an absolute, the formula of equality is both pointless and useless. The only reason it works for us is that we ignore the details of actual reality in favor of vague abstract "identities" that allow us to treat things as equal even though they aren't. And it works because the flaws in the results are also subtle, and are also ignored.
What you call "actual phenomenon" I call the "unique identity of a thing". Rest assured, we are discussing the same thing. You claim that the actual thing in all its properties cannot be equated, I say: Just so! The formula is meant to determine the truth of an equation.
More on this below...
(I see your spell-checker fixed 'equitable' but I prefer to be consistent, and besides, equitable has other connotations.)