There might be more to “naive Popperianism” than you’re making out. The testability criteria are not only intended to demarcate science, but also meaning. Of course, if it turns out that two theories which at first glance seem quite different do in fact mean the same thing, discussing “which one” is true is a category error. This idea is well-expressed by Wittgenstein:
Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question; a question only where there is an answer, and this only where something can be said.
Now, there are problems with the falsification criterion, but the more general idea that our beliefs should pay rent is a valuable one. We might think then, that the meaning of a theory is determined by the rent it can pay, and that of unobservables by their relation to the observables. A natural way to formalize this is the Ramsey-sentence:
Say you have terms for observables, O1,O2,O3,... , and for theoretical entities that aren’t observable, T1,T2,T3,... By repeated conjunction, you can combine all claims of the theory into a single sentence,
H(O1,O2,O3,...,T1,T2,T3,...)
The Ramsey-sentence then is the claim that
∃x1∃x2∃x3...H(O1,O2,O3,...,x1,x2,x3,...)
If this general idea of meaning is correct, then the Ramsey-sentence fully encompasses the meaning of the theory. If this sounds sensible so far, then the competing theories discussed here do indeed have the same meaning. The Ramsey-sentence is logically equivalent to the observable consequences of the theory being true. This is because according to the extensional characterisation of relations defined on a domain of individuals, every relation is identified with some set of subsets of the domain. The power set axiom entails the existence of every such subset and hence every such relation.
Of course, Satan and the Atlanteans are in fact motte-and-bailey arguments, and the person advocating them is likely to make claims about them on subjects other then paleontology or the pyramids that do imply different observations then the scientific consensus, and as such render their theory false straightforwardly.
There might be more to “naive Popperianism” than you’re making out. The testability criteria are not only intended to demarcate science, but also meaning. Of course, if it turns out that two theories which at first glance seem quite different do in fact mean the same thing, discussing “which one” is true is a category error. This idea is well-expressed by Wittgenstein:
Now, there are problems with the falsification criterion, but the more general idea that our beliefs should pay rent is a valuable one. We might think then, that the meaning of a theory is determined by the rent it can pay, and that of unobservables by their relation to the observables. A natural way to formalize this is the Ramsey-sentence:
Say you have terms for observables, O1,O2,O3,... , and for theoretical entities that aren’t observable, T1,T2,T3,... By repeated conjunction, you can combine all claims of the theory into a single sentence,
If this general idea of meaning is correct, then the Ramsey-sentence fully encompasses the meaning of the theory. If this sounds sensible so far, then the competing theories discussed here do indeed have the same meaning. The Ramsey-sentence is logically equivalent to the observable consequences of the theory being true. This is because according to the extensional characterisation of relations defined on a domain of individuals, every relation is identified with some set of subsets of the domain. The power set axiom entails the existence of every such subset and hence every such relation.
Of course, Satan and the Atlanteans are in fact motte-and-bailey arguments, and the person advocating them is likely to make claims about them on subjects other then paleontology or the pyramids that do imply different observations then the scientific consensus, and as such render their theory false straightforwardly.
I’m not sure that works. Imagine there are two theories about a certain button:
Pressing the button gives you a dollar and does nothing else
Pressing the button gives you a dollar and also causes an unobservable person to suffer
These theories give the same observations, but recommend different actions, so to me they seem to have different meanings.
Intended by Popper? What you are saying sounds much more like logical positivism.
Seems like you’re right. I don’t think it effects my argument though, just the name.
I don’t think the argument is strong whatever you call it.