Now, to restate the original “thing” we were trying to honestly say we had a prior for:
Suppose you know that there are a certain number of planets, N. You are unsure about the truth of a statement Q. If Q is true, you put a high probability on life forming on a given arbitrary planet. If Q is false, you put a low probability on this. You have a prior probability for Q.
Does this work, given this and our response?
We do not actually have a prior for Q, but we have a rough prior for a highly related question Q’, which can be transformed likely fairly easily into a prior for Q using mechanical methods. So let’s do that “non-mechanically” by saying:
If we successfully generate a prior for Q, that part is OK.
If Q is false, (::<- previously transformed into the more interesting and still consistent with a possible meaning for this part question “if Q is not-true”) :: use “If Q is not-true” as this proposition, then it is OK. But also consider the original meaning of “false” meaning “not true at all” meaning logically has 0 mass assigned to it. If we do both, this part is OK.
If Q is true, you put a high probability on life forming on a given arbitrary planet. This was the evidential question which we said the article was not mainly about, so we would continue reasoning from this point by reading the rest of the article until the next point at which we expect an update to occur to our prior; however if we do the rest of the steps (1-end here) then these updates can be relatively short and quick (as it’s just, in a technical sense, a multiplication. This can definitely be done by simultaneous (not just concurrent) algorithms). ::-> (predicted continuation point)
You are unsure about the truth of a statement Q. OK.
Suppose you know that there are a certain number of planets, N. This directly implies that we are only interested in the finite case and not the infinite case for N. However, we may have to keep the infinite case in mind. OK.
-> [Now to be able to say “we have a prior,” we have to write the continuation from 3. until the meaning of both
“what the article is about” becomes clear (so we can disambiguate the intended meanings of 1-5 and re-check)
We recognise that the prior can be constructed, and can roughly describe what it would look like.
From our previous response, our prior for finite N and a small amount of evidence was that “life is unlikely” (because there were two separate observationally consistent ways which resulted in ‘the same’ answer in some equivalence or similarity sense). For infinite N, it looks like “n is of lower dimension in some way” (dimension here meaning “bigness”) than N.
Now we have a prior for both, so we can try to convert back to a prior for the original proposition Q, which was:
You are unsure about the truth of a statement Q. If Q is true, you put a high probability on life forming on a given arbitrary planet. If Q is false, you put a low probability on this.
Our prior is that Q is false.]
In retrospect, the preceding (now in square brackets, which were edited in) could be considered a continuation of 3. So we are OK in all 5 ways, and we have a prior, so we can continue responding to the article.
Now, to restate the original “thing” we were trying to honestly say we had a prior for:
Does this work, given this and our response?
We do not actually have a prior for Q, but we have a rough prior for a highly related question Q’, which can be transformed likely fairly easily into a prior for Q using mechanical methods. So let’s do that “non-mechanically” by saying:
If we successfully generate a prior for Q, that part is OK.
If Q is false, (::<- previously transformed into the more interesting and still consistent with a possible meaning for this part question “if Q is not-true”) :: use “If Q is not-true” as this proposition, then it is OK. But also consider the original meaning of “false” meaning “not true at all” meaning logically has 0 mass assigned to it. If we do both, this part is OK.
If Q is true, you put a high probability on life forming on a given arbitrary planet. This was the evidential question which we said the article was not mainly about, so we would continue reasoning from this point by reading the rest of the article until the next point at which we expect an update to occur to our prior; however if we do the rest of the steps (1-end here) then these updates can be relatively short and quick (as it’s just, in a technical sense, a multiplication. This can definitely be done by simultaneous (not just concurrent) algorithms). ::-> (predicted continuation point)
You are unsure about the truth of a statement Q. OK.
Suppose you know that there are a certain number of planets, N. This directly implies that we are only interested in the finite case and not the infinite case for N. However, we may have to keep the infinite case in mind. OK.
-> [Now to be able to say “we have a prior,” we have to write the continuation from 3. until the meaning of both
“what the article is about” becomes clear (so we can disambiguate the intended meanings of 1-5 and re-check)
We recognise that the prior can be constructed, and can roughly describe what it would look like.
From our previous response, our prior for finite N and a small amount of evidence was that “life is unlikely” (because there were two separate observationally consistent ways which resulted in ‘the same’ answer in some equivalence or similarity sense). For infinite N, it looks like “n is of lower dimension in some way” (dimension here meaning “bigness”) than N.
Now we have a prior for both, so we can try to convert back to a prior for the original proposition Q, which was:
Our prior is that Q is false.]
In retrospect, the preceding (now in square brackets, which were edited in) could be considered a continuation of 3. So we are OK in all 5 ways, and we have a prior, so we can continue responding to the article.
(To be continued in reply)