there is two ways ‘theory’ is used that are different and often lead to confusion.
Theory in thescientific sense the way a physicist would use: it’s a model of the world that is either right or wrong. there might be competing theories and we neeed to have empirical evidence to figure out which one’s right. Ideally, they agree with empirical evidence or at least are highly falsifiable. Importantly, if two theories are to conflict they need to actually speak about the same variables, the same set of measurable quantities.
Theory in the mathematician’ sense; a formal framework There is a related but different notion of theory that a mathematician would use: a theory of groups, of differential equations, of randomness, of complex systems, of etc etc. This is more like a formal framework for a certain phenomenon or domain. It defines what the quantities, variables, features one is interested in even are.
One often hears the question whether this (mathematical) theory makes testable predictions. This sounds sensible but doesn’t really makes sense. It is akin to asking whether arithmetic or calculus makes testable predictions.*
Theories in the mathematician’s sense can’t really be wrong or right since (at least in theory) everything is proven. Of course, theories in this sense can fail to say much about the real world, they might bake in unrealistic assumptions of course etc.
Other uses of ‘Theory’
The world ‘theory’ is also used in other disciplines. For instance, in literature studies where it is a denotes free form vacuous verbiage; or in ML where ‘theory’ it is used for uninformed speculation.
*one could argue that the theory of Peano Arithmetic actually does make predictions about natural numbers in the scientific sense, and more generally theories in the mathematical sense in a deep sense really are theories in the scientific sense. I think there is something to this but 1. it hasn’t been developed yet 2. mostly irrelevant in the present context.
Formal frameworks considered in isolation can’t be wrong. Still, they often come with some claims like “framework F formalizes some intuitive (desirable?) property or specifies the right way to do some X and therefore should be used in such-and-such real-world situations”. These can be disputed and I expect that when somebody claims like “{Bayesianism, utilitarianism, classical logic, etc} is wrong”, that’s what they mean.
There’s a related confusion between uses of “theory” that are neutral about the likelihood of the theory being true, and uses that suggest that the theory isn’t proved to be true.
Cf the expression “the theory of evolution”. Scientists who talk about the “theory” of evolution don’t thereby imply anything about its probability of being true—indeed, many believe it’s overwhelmingly likely to be true. But some critics interpret this expression differently, saying it’s “just a theory” (meaning it’s not the established consensus).
On the word ‘theory’.
The word ‘theory’ is oft used and abused.
there is two ways ‘theory’ is used that are different and often lead to confusion.
Theory in thescientific sense
the way a physicist would use: it’s a model of the world that is either right or wrong. there might be competing theories and we neeed to have empirical evidence to figure out which one’s right. Ideally, they agree with empirical evidence or at least are highly falsifiable. Importantly, if two theories are to conflict they need to actually speak about the same variables, the same set of measurable quantities.
Theory in the mathematician’ sense; a formal framework
There is a related but different notion of theory that a mathematician would use: a theory of groups, of differential equations, of randomness, of complex systems, of etc etc. This is more like a formal framework for a certain phenomenon or domain.
It defines what the quantities, variables, features one is interested in even are.
One often hears the question whether this (mathematical) theory makes testable predictions. This sounds sensible but doesn’t really makes sense. It is akin to asking whether arithmetic or calculus makes testable predictions.*
Theories in the mathematician’s sense can’t really be wrong or right since (at least in theory) everything is proven. Of course, theories in this sense can fail to say much about the real world, they might bake in unrealistic assumptions of course etc.
Other uses of ‘Theory’
The world ‘theory’ is also used in other disciplines. For instance, in literature studies where it is a denotes free form vacuous verbiage; or in ML where ‘theory’ it is used for uninformed speculation.
*one could argue that the theory of Peano Arithmetic actually does make predictions about natural numbers in the scientific sense, and more generally theories in the mathematical sense in a deep sense really are theories in the scientific sense. I think there is something to this but 1. it hasn’t been developed yet 2. mostly irrelevant in the present context.
Formal frameworks considered in isolation can’t be wrong. Still, they often come with some claims like “framework F formalizes some intuitive (desirable?) property or specifies the right way to do some X and therefore should be used in such-and-such real-world situations”. These can be disputed and I expect that when somebody claims like “{Bayesianism, utilitarianism, classical logic, etc} is wrong”, that’s what they mean.
There’s a related confusion between uses of “theory” that are neutral about the likelihood of the theory being true, and uses that suggest that the theory isn’t proved to be true.
Cf the expression “the theory of evolution”. Scientists who talk about the “theory” of evolution don’t thereby imply anything about its probability of being true—indeed, many believe it’s overwhelmingly likely to be true. But some critics interpret this expression differently, saying it’s “just a theory” (meaning it’s not the established consensus).