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RobbBB comments on Request for Steelman: Non-correspondence concepts of truth - Less Wrong
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I'd say there are three phenomena going on:
There are specific problems with correspondence theory -- what do mathematical truths correspond to? moral truths? modal truths? vague truths? -- which either cause philosophers to reject correspondence theory in more classical domains, or cause them to adopt an ersatz theory where some truths depend on correspondence and some depend on other things. (This is approximately where I am, and arguably makes me a rejector of 'correspondence theory,' though I accept it in the mundane contexts LWers generally mean it.)
There are some people who really do just have silly views like 'there's nothing outside of our experiences' or the more respectable 'reality outside our experiences is ineffable' (thanks to Berkeley, Kant, and various mystics). There is then a larger pool of people who don't quite hold those beliefs, but believe they believe in them, or (more accurately) have positive associations with asserting those statements in arguments.
Most other people probably just have different interests/goals, and these are being misconstrued as a disagreement. Some people think it would be interesting or useful or elegant to define 'truth' in a way that makes us keep the Real World in mind; others think it would be interesting or useful or elegant to define 'truth' in a way that makes it reasonable proxy for 'epistemic praiseworthiness', so that even a systematically deceived agent could still be given a 'truth' ranking that matches its level of revealed virtue. These may both be good concepts to have a name for, and which one (if either) we call 'truth' is not so important.
Steel-manning group 1 means talking about the problem cases where correspondence theory seems to break down, while granting the general point that there is a universe outside my head and there's some fashion in which the assertion-conditions for many of my ordinary statements depend on how the world is. A group 2 steel-man might look like an exotic simulation hypothesis -- perhaps combined with rejecting Chalmers' theory of skeptical hypotheses in The Matrix as Metaphysics. A group 3 steel-man would involve reasonably, explicitly discussing the pragmatic value of different conceptions of truth, relative to our linguistic needs and history.
Mathematical reality.
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.
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,