If my model says the sky should be blue, and I go out and look and the sky is blue, my model corresponds to reality.
It corresponds to appearance. Models posit causal mechanisms, and the wrong mechanism can predict the right observations.
In general, the correspondence theory of truth means that a proposition is true when reality, or some chunk of reality, is the way the proposition says it is. Translating that as directly as possible into physical science, a science, a theory would be true if it's posits, the things it claims exist, actually exist. For instance, the phlogiston theory is true if something with the properties of phlogiston exists. The important thing is that correspondence in that sense, let's say "correspondence of ontological content", is not the same as predictive accuracy. To be sure, a theory would that is not empirically predictive is rejected as being ontological inaccurate as well.....but that does not mean empirical predictiveness is a sufficient criterion of ontological accuracy...we cannot say that a theory tells it like it is, just because it allows us to predict observations.
For one thing, instrumentalists and others who interpret science non realistically, still agree that theories are rendered true other false by evidence,
Another way of making this point is that basically wrong theories can be very accurate. For instance, the Ptolemaic system can be made as accurate as you want for generating predictions, by adding extra epicycles ... although it is false, in the sense of lacking ontological accuracy, since epicycles don't exist.
Another way, still, is to notice that theories with different ontologies can make equivalent predictions, like wave particle duality in physics.
The fourth way is based on sceptical hypotheses, such as Brain in a Vat and the Matrix. Sceptical hypotheses can be rejected, for instance by appeals to Occams Razor, but they cannot be refuted empirically, since any piece of empirical evidence is subject to sceptical interpretation. Occams's Razor is not empirical
Science conceives of perception as based in causation, and causation as being comprised of chains of causes and effects, with only the ultimate effect, the sensation evoked in the observer, being directly accessible to the observer. The cause of the sensation, the other end of the causal chain, the thing observed, has to be inferred from the sensation, the ultimate effect -- and it cannot be inferred uniquely, since, in general, more than one cause can produce the same effect. All illusions, from holograms to stage conjuring, work by producing the effect, the percept, in an unexpected way. A BIV or Matrix observer would assume that the precept of a horse is caused by a horse, but it would actually by a mad scientist pressing buttons.
A BIV or Matrix observer could come up with science that works, that is useful, for many purposes, so long as their virtual reality had some stable rules. They could infer that dropping an (apparent) brick onto their (apparent) foot would cause pain, and so on. It would be like the player of a computer game being skilled in the game. But the workability of their science is limited to relating apparent causes to apparent effects, not to grounding causes and effects in ultimate reality.
A couple of days ago, Buybuydandavis wrote the following on Less Wrong:
I've spent a lot of energy over the last couple of days trying to come to terms with the implications of this sentence. While it certainly corresponds with my own observations about many people, the thought that most humans simply reject correspondence to reality as the criterion for truth seems almost too outrageous to take seriously. If upon further reflection I end up truly believing this, it seems that it would be impossible for me to have a discussion about the nature of reality with the great majority of the human race. In other words, if I truly believed this, I would label most people as being too stupid to have a real discussion with.
However, this reaction seems like an instance of a failure mode described by Megan McArdle:
With this background, it seems important to improve my model of people who reject correspondence as the criterion for truth. The obvious first place to look is in academic philosophy. The primary challenger to correspondence theory is called “coherence theory”. If I understand correctly, coherence theory says that a statement is true iff it is logically consistent with “some specified set of sentences”
Coherence is obviously an important concept, which has valuable uses for example in formal systems. It does not capture my idea of what the word “truth” means, but that is purely a semantics issue. I would be willing to cede the word “truth” to the coherence camp if we agreed on a separate word we could use to mean “correspondence to reality”. However, my intuition is that they wouldn't let us to get away with this. I sense that there are people out there who genuinely object to the very idea of discussing whether a sentences correspond to reality.
So it seems I have a couple of options:
1. I can look for empirical evidence that buybuydandavis is wrong, ie that most people accept correspondence to reality as the criterion for truth
2. I can try to convince people to use some other word for correspondence to reality, so they have the necessary semantic machinery to have a real discussion about what reality is like
3. I can accept that most people are unable to have a discussion about the nature of reality
4. I can attempt to steelman the position that truth is something other than correspondence
Option 1 appears unlikely to be true. Option 2 seems unlikely to work. Option 3 seems very unattractive, because it would be very uncomfortable to have discussions that on the surface appear to be about the nature of reality, but which really are about something else, where the precise value of "something else" is unknown to me.
I would therefore be very interested in a steelman of non-correspondence concepts of truth. I think it would be important not only for me, but also for the rationalist community as a group, to get a more accurate model of how non-rationalists think about "truth"