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 nonstandard 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’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 nonstandard 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.