gedymin

How do you evaluate whether any given model is useful of not?

One way is to simulate a perfect computational agent, assume perfect information, and see what kind of models it would construct.

If you reject the notion of an external reality that is accessible to us in at least some way, then you cannot really measure the performance of your models against any kind of a common standard.

Solomonoff induction provides a universal standard for "perfect" inductive inference, that is, learning from observations. It is not entirely parameter-free, so it's "a standard", not "the standard". I doubt if there is *the* standard for the same reasons I doubt that Platonic Truth does exist.

All you've got left are your internal thoughts and feelings

Umm, no, this is a false dichotomy. There is a large area in between "relying on one's intuition" and "relying on an objective external word". For example, how about "relying on the accumulated knowledge of others"?

See also my comment in the other thread.

I've got feeling that the implicit LessWrong'ish rationalist theory of truth is, in fact, some kind of epistemic (Bayesian) pragmatism, i.e. "true is that what is knowable using probability theory". May also throw in "..for a perfect computational agent".

My speculation is that the declared LW's sympathy towards the correspondence theory of truth stems from political / social reasons. We don't want to be confused with the uncritically thinking masses - the apologists of homoeopathy or astrology justifying their views by "yeah, I don't know how it works either, but it's *useful*!"; the middle-school teachers who are ready to threat scientific results as epistemological equals of their favourite theories coming from folk-psychology, religious dogmas, or "common sense knowledge", because, you known, "they all are true in some sense". Pragmatic theories of truth are dangerous if they come into the wrong hands.

What do you mean by "direct access to the world"?

Are you familiar with Kant? http://en.wikipedia.org/wiki/Noumenon

This description fits philosophy much better than science.

Sounds like a form of abduction, or, more precisely, failure to consider alternative hypotheses.

As for your options, have you considered the possibility that 99% of people have never formulated a coherent philosophical view on the theory of truth?

I'd love to hear a more qualified academic philosopher discuss this, but I'll try. It's not that the other theories are intuitively appealing, it's that the correspondence theory of truth has a number of problems, such as the problem of induction.

Let's say the one day we create a complete simulation of a universe where the physics almost completely match ours, except some minor details, such as that some specific types of elementary particles, e.g. neutrinos are never allowed to appear. Suppose that there are scientists in the simulation, and they work out the Standard Model of their physics. The model presupposes existence of neutrinos, but their measurement devices are never going to interact with a neutrino. Is the statement "neutrinos exist" true or false from their point of view? I'd say that the answer is "does not matter". To turn the example around, can we be sure that aether does not exist? Under Bayesianism, every instance of scientists *not* observing aether increases our confidence. However we might be living in a simulation where the simulators have restricted all observations that could reveal the existence of aether. So it cannot be completely excluded that aether exists, but is unobservable. So the correspondence theory is forced to admit that "aether exists" has an unknown truth value. In contrast, a pragmatic theory of truth can simply say that anything that cannot, in principle, be observed by any means also *does not exist*, and be fine with that.

Ultimately, the correspondence theory presupposes a deep Platonism as it relies on the Platonic notion of Truth being "somewhere out there". It renders science vulnerable to problem of induction (which is not a real problem as far as real world is concerned) - it allows anyone to dismiss the scientific method off-handedly by saying that "yeah, but science cannot really arrive at the Truth - already David Hume proved so!"

We have somehow to deal with the possibility that everything we believe might turn out to be wrong (e.g. we are living in a simulation, and the real world has completely different laws of physics). Accepting correspondence theory means accepting that we are not capable of reaching truth, and that we are not even capable of knowing if we're moving in the direction of truth! (As our observations might give misleading results.) A kind of philosophical paralysis, which is solved by the pragmatic theory of truth.

There's also the problem that categories really do not exist in some strictly delineated sense; at least not in natural languages. For example consider the sentences in form "X is a horse". According to correspondence, a sentence from this set is true iff X is a horse. That seems to imply that X must be a mammal of genus *Equus* etc. - something with flesh and bones. However, one can point to a picture of a horse and say "this is a horse", and would not normally be considered lying. Wittgenstein's concept of family resemblance comes to rescue, but I suspect does not play nicely with the correspondence theory.

Finally, there's a problem with truth in formal systems. Some problems in some formal systems are known to be unsolvable; what is the truth value of statements that expand to such a problem? For example, consider the formula G (from Goedel's incompleteness theorem) expressed in Peano Arithmetic. Intuitively, G is true. Formally, it is possible to prove that assuming G is true does not lead to inconsistencies. To do that, we can provide a model of Peano Arithmetic using this standard interpretation. The standard set of integers is an example of such a model. However, it is also possible to construct *non*standard models of Peano Arithmetic extended with negation of G as an axiom. So assuming that negation of G is true *also* does not lead to contradictions. So we're back at the starting point - is G true? Goedel thought so, but he was a mathematical Platonist, and his views on this matter are largely discredited by now. Most do not believe that G has a truth value is some absolute sense.

This aspect together with Tarki's undefinability theorem suggest that is might not make sense to talk about unified mathematical Truth. Of course, formal systems are not the same as the real world, but the difficulty of formalizing truth in the former increases my suspicion of formalizations / axiomatic explanations relevant to in the latter.

I meant that as a comment to this:

the information less useful than what you'd get by just asking a few questions.

It's easy to lie when answering to questions about your personality on e.g. a dating site. It's harder, more expensive, and sometimes impossible to lie via signaling, such as via appearance. So, even though information obtained by asking questions is likely to be much richer than information obtained from appearances, it is also less likely to be truthful.

..assuming the replies are truthful.

I agree with pragmatist (the OP) that this is a problem for the correspondence theory of truth.

Usefulness? Just don't say "experimental evidence". Don't oversimplify epistemic justification. There are many aspects - how well knowledge fits with existing models, with observations, what is it's predictive power, what is it's instrumental value (does it help to achieve one's goals) etc. For example, we don't have

anyexperimental evidence that smoking causes cancer in humans, but we nevertheless believe that is does. The power of Bayesian approach is in the mechanism to fuse together all these different forms of evidence and to arrive at a single posterior probability.