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RobbBB comments on Request for Steelman: Non-correspondence concepts of truth - Less Wrong
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Can you be more specific? Is '2+2=4' true in virtue of literal mathematical objects like '2' and '4'? If so, how do those objects causally relate to my assertion that 2 and 2 makes 4, or to the evidence underlying that assertion?
Because they cause there to four apples in a box if you put two apples in, and then put two more apples in.
If both you and a sentient alien in another galaxy write out addition tables, the two tables will be highly correlated with each other (in fact they'll correspond). Which means that either one caused the other, or both have a common cause. What's the common cause, the laws of mathematics.
So maths is physics.
But I can write an equation for an inverse cube law of gravity, which doesn't apply to this universe. What does it correspond to?
Not quite, although I agree the approach I describe also applies to establish that the laws of physics exist.
Yes, and if you and the alien both write down a cube law and predict what orbits would be like in a universe where it were true, you would reach the same conclusions.
That doesn't establish that mathematics is true by correspondence,.
So what would you describe as the cause of the correlation in the orbits calculated by myself and the alien?
Running off the same axioms and references rules).
In a sense that means the same laws, but the laws are not independently existing entities that mathematical truths correspond to.
In the Philip K. Dick sense they are.
In the PKD sense, they are not, because finitists and constructivists adopt different axioms able get different results,
No, you can write out an equation using suggestively named variables like "G" and "m" and "r". The second the equation stops modeling the strength of the gravitational force, however, it ceases to be a "law of gravity", regardless of what letters you used for the variables. It's just some random equation.
That amounts to saying that what isnt physically true isnt physically true . The point, however, is that what is not physically true can be mathematically true, so mathematical truth cannot consist of correspondence to the physical world,