Reply: The abstract concept of ‘truth’ - the general idea of a map-territory correspondence—is required to express ideas such as: …
Is this true? Maybe there’s a formal reason why, but it seems we can informally represent such ideas without the abstract idea of truth. For example, if we grant quantification over propositions,
Generalized across possible maps and possible cities, if your map of a city is accurate, navigating according to that map is more likely to get you to the airport on time.
becomes
Generalized across possible maps and possible cities, if your map of a city says “p” if and only iff p, navigating according to that map is more likely to get you to the airport on time.
To draw a true map of a city, someone has to go out and look at the buildings; there’s no way you’d end up with an accurate map by sitting in your living-room with your eyes closed trying to imagine what you wish the city would look like.
becomes
To draw a map of a city such that the map says “p” if and only if p, someone has to go out and look at the buildings; there’s no way you’d end up with a map that says “p” if and only if p by sitting in your living-room with your eyes closed trying to imagine what you wish the city would look like.
True beliefs are more likely than false beliefs to make correct experimental predictions, so if we increase our credence in hypotheses that make correct experimental predictions, our model of reality should become incrementally more true over time.
becomes
Beliefs of the form “p”, where p, are more likely than beliefs of the form “p”, where it is not the case that p, to make correct experimental predictions, so if we increase our credence in hypotheses that make correct experimental predictions, our model of reality should incrementally contain more assertions “p” where p, and fewer assertions “p” where not p, over time.
Generalized across possible maps and possible cities, if your map of a city says “p” if and only iff p
If you can generalize over the correspondence between p and the quoted version of p, you have generalized over a correspondence schema between territory and map, ergo, invoked the idea of truth, that is, something mathematically isomorphic to in-general Tarskian truth, whether or not you named it.
Well, yeah, we can taboo ‘truth’. You are still using the titular “useful idea” though by quantifying over propositions and making this correspondence. The idea that there are these things that are propositions and that they can appear both in quotation marks and also appear unquoted, directly in our map, is a useful piece of understanding to have.
Is this true? Maybe there’s a formal reason why, but it seems we can informally represent such ideas without the abstract idea of truth. For example, if we grant quantification over propositions,
becomes
Generalized across possible maps and possible cities, if your map of a city says “p” if and only iff p, navigating according to that map is more likely to get you to the airport on time.
becomes
To draw a map of a city such that the map says “p” if and only if p, someone has to go out and look at the buildings; there’s no way you’d end up with a map that says “p” if and only if p by sitting in your living-room with your eyes closed trying to imagine what you wish the city would look like.
becomes
Beliefs of the form “p”, where p, are more likely than beliefs of the form “p”, where it is not the case that p, to make correct experimental predictions, so if we increase our credence in hypotheses that make correct experimental predictions, our model of reality should incrementally contain more assertions “p” where p, and fewer assertions “p” where not p, over time.
If you can generalize over the correspondence between p and the quoted version of p, you have generalized over a correspondence schema between territory and map, ergo, invoked the idea of truth, that is, something mathematically isomorphic to in-general Tarskian truth, whether or not you named it.
Well, yeah, we can taboo ‘truth’. You are still using the titular “useful idea” though by quantifying over propositions and making this correspondence. The idea that there are these things that are propositions and that they can appear both in quotation marks and also appear unquoted, directly in our map, is a useful piece of understanding to have.