As I see it, statements start with some probability of being true propositions, some probability of being false propositions, and some probability of being neither. So a statement about which I have no information, say a random statement to which a random number generator was designed to preface with “Not” half the time, has a less than 50% chance of being true.
This speaks to the intuition that statements fail to be true most of the time. “A proposition, any proposition, starts out with a 50% probability of being true” is only true assuming the given statement is a proposition, and I think knowing that an actual statement is a proposition entails being contaminated by knowledge about the proposition’s contents.
As I see it, statements start with some probability of being true propositions, some probability of being false propositions, and some probability of being neither.
Okay. So “a statement, any statement, is as likely to be true as false (under total ignorance)” would be more accurate. The odds ratio remains the same.
The intuition that statements fail to be true most of the time is wrong, however. Because, trivially, for every statement that is true its negation is false and for every statement that is false its negation is true. (Statements that have no negation are neither true nor false)
It’s just that (interesting) statements in practice tend to be positive claims (about the world), and it’s much harder to make a true positive claim about the world than a true negative one. This is why a long (measured in Kolmogorov complexity) positive claim is very unlikely to be true and a long negative claim (Kolmogorov complexity) is very likely to be true. Also, it’s why a long conjunction of terms is unlikely to be true and a long disjunction of terms is likely to be true. Again, symmetry.
S -> statements
P -> propositions
N -> non-propositional statements
T -> true propositions
F -> false propositions
I don’t agree with condition S = ~T + T.
Because ~T + T is what you would call the set of (true and false) propositions, and I have readily accepted the existence of statements which are neither true nor false. That’s N. So you get S = ~T + T + N = T + F + N = P + N
We can just taboo proposition and statement as proposed by komponisto. If you agree with the way he phrased it in terms of hypothesis then we’re also in agreement (by transitivity of agreement :)
(This may be redundant, but if your point is that the set of non-true statements is larger than the set of false propositions, then yes, of course, I agree with that. I still don’t think the distinction between statement and proposition is that relevant to the underlying point because the odds ratio is not affected by the inclusion or exclusion of non-propositional statements)
What’s the relevance of this question? Is there a reason “statement” shouldn’t be interpreted as “proposition” in the above?
As I see it, statements start with some probability of being true propositions, some probability of being false propositions, and some probability of being neither. So a statement about which I have no information, say a random statement to which a random number generator was designed to preface with “Not” half the time, has a less than 50% chance of being true.
This speaks to the intuition that statements fail to be true most of the time. “A proposition, any proposition, starts out with a 50% probability of being true” is only true assuming the given statement is a proposition, and I think knowing that an actual statement is a proposition entails being contaminated by knowledge about the proposition’s contents.
Okay. So “a statement, any statement, is as likely to be true as false (under total ignorance)” would be more accurate. The odds ratio remains the same.
The intuition that statements fail to be true most of the time is wrong, however. Because, trivially, for every statement that is true its negation is false and for every statement that is false its negation is true. (Statements that have no negation are neither true nor false)
It’s just that (interesting) statements in practice tend to be positive claims (about the world), and it’s much harder to make a true positive claim about the world than a true negative one. This is why a long (measured in Kolmogorov complexity) positive claim is very unlikely to be true and a long negative claim (Kolmogorov complexity) is very likely to be true. Also, it’s why a long conjunction of terms is unlikely to be true and a long disjunction of terms is likely to be true. Again, symmetry.
S=P+N
P=T+F
T=F
S=~T+T
N>0
~~~
~T+T=P+N
~T+T=T+F+N
~T=F+N
~T=T+N
~T>T
Legend:
I don’t agree with condition S = ~T + T.
Because ~T + T is what you would call the set of (true and false) propositions, and I have readily accepted the existence of statements which are neither true nor false. That’s N. So you get S = ~T + T + N = T + F + N = P + N
We can just taboo proposition and statement as proposed by komponisto. If you agree with the way he phrased it in terms of hypothesis then we’re also in agreement (by transitivity of agreement :)
(This may be redundant, but if your point is that the set of non-true statements is larger than the set of false propositions, then yes, of course, I agree with that. I still don’t think the distinction between statement and proposition is that relevant to the underlying point because the odds ratio is not affected by the inclusion or exclusion of non-propositional statements)