i suppose i was thinking a little bit about "truth-preserving" operations and "truth-finding" operations. maybe the latter is better than the former. the context was a discussion in NONSPECIFIC DISCORD about llm's and ai not producing correct answers generally (and then also how people tend to expect right answers), and PERSON X made the point that "true" isn't what's being measured or created, what's being measured and created is a phrase that is close to phrases that have been said. and my thought, which i nearly said there but then i decided it wasn't really my conversation to interject in, was that of course the results aren't generally true. there is no reason to expect them to be generally true. the thing that is being done, the process by which the thing is being made, is not dependent on the truth of the output almost at all. for very simple things, you expect true answers maybe more often than not because many people have said true things on the subject before. but for unique or rare things.... there's just no reason why this would produce true outputs. there's no reason it would produce a meaningful output, really. in human discursive life, in the sciences in mathematics in things like these, a conversation happens, a claim is made, and then by some established procedure, the claim is measured against whatever the standard of "truth" for the subject happens to be.
in math, this is "can you produce a proof that is (or appears to other professionals to be) logically sound", and in such a case, the thing you said gets to be called "truth" and people get to behave as though they believe it in full confidence, in the setting of professional mathematics. in the sciences, the standard is "stands up to experimental verification, up to a set tolerance for experimental uncertainty, and also has some form of theoretical justification which is coherent with existing models from the science, or proposes a new model which is coherent with the general model-building practices of the field". since i am not a scientist in any of the physical sciences, i have a very modest sense of what the latter portion of this, on model coherence and model-building, really entails. but that is my sense of things. we expect that this type of process produces outputs which are sensibly called "true", because when we say something is "true" in the context of the sciences, what we mean by true is almost exactly this: something is "true" in the sense of physics if it matches observations of reality, i.e. if it matches experimentation now and later, something is "true" in the sense of mathematics if it can be proven from the agreed-upon principles using the methods of logical deduction. we then export "true-in-this-sense" to "true-as-a-fact", which is perhaps dicey but also perhaps sensible. if something is "true" in the sense of physics, then it is expected to match experimental reality. if something matches experimental reality in practice, then you can build things with it. that is, if something is "true" in the sense of physics, then you can use it to make things. which we do. and they tend to work. because the standards of "true" for physics match up almost exactly to what we need something "true" in reality to be, if it is to be useful to us in making things.
this sense of truth is tailor-made to the practice of its use. in mathematics, there is a further abstraction before its application. but the abstraction is essentially that it goes through physics, that the mathematics we do seems to match up to what we produce from physics. then we study the systems of math that we generate by looking at physics, we develop calculus, theories of functions, things of this sort. and they can take on a life of their own. then, once math is robust enough to have its own character feasibly, it has its own character actually: the rules of mathematical derivation and verification match up to how math is applied; you compute, you transit equalities, you transit inequalities, you transit implications, and so on. once you notice that these operations are functional for the sake of doing the things you want math applied for, they are ready to become studies of their own: what can be said of operations that transit "like equality", that behave "like addition", about geometries that look like pieces of the abstractions of geometry we produce from inspecting curvature, inspecting coordinate systems, radio waves. so again, we have a version of "truth" which is, albeit through an added layer of abstraction, still essentially built from use. so it is used. so it is useful. in the case of llm's, for example, the process is not a thing of this sort. it is not producing an output which is then measured against a standard for "truth", and further it is not being measured against a standard of "truth" which derives from practice or from applications. it is measured against a standard of "looks like something a person might say", more or less. there is not a line from application to truth-standard, there is not even obviously a truth-standard to begin with.