This post has taken a few hours to put together, so thanks for the challenge. I hope you find it as interesting as I do. — Banno
Interesting and stimulating, it has put my mind in such a state of agitation.
Response nonetheless:
"116 When philosophers use a word - "knowledge", "being", "object", "I", "proposition", "name" - and try to grasp the essence of the thing, one must always ask oneself: is the word ever actually used in this way in the language-game which is its original home?- What we do is to bring words back from their metaphysical to the everyday use." Wittgenstein, PI
In this spirit, along with my reaction to your's and others feedback, I believe I need to take a little more creative approach. I like to borrow, roughly, an approach Quine performed in Word and Object around his treatment of time. In previous post I presented three scientific equations:
1. E = Mc²
2. X = vt + Xi
3. 1/2Mv^2 = 3/2RT
Special attention was given to the symbol "=" that I believe gave way to talk of "identity" and "equivalence". After much thought, I started thinking this symbol was creating some problems. One, it was leading one to think there must be some similarity to logicians use of "a = a". Two, this symbol was distracting the actual meaning of these scientific expressions. Lastly, and obviously, its persistent use in mathematics may lead one to think this may be the ultimate meaning of these equations, "numeric value" is equal "numeric value".
Given these concerns, I think it best to leave behind the symbol "=" and use another, "⇔"
1. E ⇔ Mc²
2. X ⇔ vt + Xi
3. 1/2Mv^2 ⇔ 3/2RT
This different symbol is to emphasize what the relationship between both side of the equation. Let's take the simpler of the three equations, #2.
What is this scientific equation trying to express: For experimentally determine values of variables v, t, and Xi, where v is average velocity, t is duration of time, and Xi is the initial object's position, the object's final position is determined by v multiplied by t plus Xi. So, if you determine v, t, and Xi, you can predict X. Consider, equation #3, if you determine the temperature, you can predict the kinetic energy of the gas, or vice versa if you determine the kinetic energy of the gas, you can predict the temperature of the gas. Notice, there is no need to call these expressions as some kind of identity statement. This is just to introduce some metaphysical baggage that is not needed for these equations to function.
Historically, scientists established these equations well before the creation of S5 modal logic. What exactly is Kripke's value in calling them identity statements? That when we of talking about object's initial position and final position, we, by metaphysical necessity, must be talking about the same object. But this seems to be a troublesome expectation. What if the final position is not as we predicted, should we, as you say, "reject counter instances as errors of identification." No, we should proceed as scientists would do in these cases, see if we made some error in measuring, or maybe the instrumentation malfunctioned. But could you not say that you made an error by measuring the incorrect object? Sure, but I also could have measure the wrong object and found the position to be what was expected, and this just demonstrates that this has nothing to do with metaphysical necessity.
"124 Philosophy may in no way interfere with the actual use of language; it in the end only describe it." PI 124