Thanks, Paul the Uncertain. I appreciate your background in describing different approaches as different ways of managing uncertainty. It is a perspective that seems to me to highlight the fact that the same circumstances and similar patterns of reasoning can be described in different ways.
One easy example of this is to consider propositional logic and its extension, first order logic. Already, first order logic provides different ways of describing arguments in simple propositional logic: for example, the premise P, "Socrates is a man," can be represented by the predicate "is_man(Socrates)" and the premise Q, "all men are mortal," can be represented with a universal quantifier. And while we can see these kinds of equivalences, it's also not hard to imagine someone choosing to use the (less powerful) propositional logic. It is simpler and thus easier to explain your thoughts in for a non-technical audience, for example. And there are many different extensions or even mutually inconsistent versions of logic, so perhaps some of them are counter-intuitive or detract from the message of an argument. (For example, nobody would use a paraconsistent logic unless they wanted to emphasize that they tolerate some contradictions to arrive in their system.)
Likewise, nobody would use probabilistic statements unless they wanted to emphasize that some of the propositions they're describing do not have perfect certainty.
Indeed we may find people even permitting a little higher order, philosophical dissonance in order to reduce the amount of miscommunication regarding their emphasis with regards to the lower order, practical flow of representation of their particular arguments.
For example, it's common for people to recognize that their statements are fallible. What does that mean? Their statements are not logically entailed by their evidence. There is a logical gap between the evidence they have and the statements they are willing to assert as beliefs. For example, there is a logical gap between my evidence "I have a memory of having oatmeal this morning" and my belief "I had oatmeal this morning." The major premise connecting them is something like "I can rely on my memory in these kinds of circumstances," but there's no absolute certainty that the human system of memory never fails. And yet to me it's a bit absurd to imagine that I didn't have oatmeal. The memory makes it seem close enough to a certainty to me, that it would be misleading and introduce noise into the conversation for me to speak of anything less than some kind of rounding error of full certainty regarding my credence here.
For all practical purposes, I would in certain contexts be willing to represent this credence of mine as having probability "1" even though I am fallible. Perhaps this would simplify later considerations for me: should I spend energy entertaining possible timelines where I didn't have oatmeal? I don't think so. And if I am not going to do so, there is a practical argument for representing this credence with 1; it lets me move on and not continually consider the probability space of worlds where I did not have oatmeal. This lowers the cost of the effort to be rational with an entirely acceptable trade-off that I have excluded some possibilities even though my knowledge is fallible. It has the further benefit of being less confusing to other people. If I said something else, I would be drawing attention to the vanishing small and theoretical possibility (from my perspective) that I didn't have oatmeal, which makes me sound a bit like a skeptic rather than someone who claims to have knowledge.
So, yes, I agree with several of the points you have made, Paul (if I understood them):
(1) It is coherent to use credences of 0 and 1, including when using the evidential / subjective interpretation of probability.
(2) A key feature of subjective probability is that it is conditioned on the evidence available and considered when the credence is formed: my credence that I had oatmeal, for example, is based on my memory, while any reader of this post has only my testimony.
(3) There are different systems for describing reasoning under uncertainty (and certainty). There is no one system of description that everyone uses all the time.
These are, I think, matters of clarification.
A key underlying subject of dispute, as I see it, is whether the past (even while undertaking some activity of describing the past called "history") can coherently be described in terms that use the evidential interpretation of probability. I think that it can, but I would welcome an argument that shows that it can't. So far the only valid argument that I have seen here is the idea that we have to be using the frequentist interpretation of probability (if we refer to probability), which would be a successful and sound argument if the premise were true. But I don't agree with the premise. So I have argued against dogmatic frequentism.
And even though this is the only argument with valid logic and no misunderstandings that I have seen here, I am also getting the sense that maybe nobody is explicitly defending this argument. There is a distinct possibility that my defense of the viability of the evidential interpretation of probability may end up a little bit neglected, as if irrelevant, because the premises of the argument being made -- e.g., dogmatic frequentism when it comes to the interpretation of probability -- are not fully understood by those making the argument themselves.
Does anyone want to come to the defense of frequentism as the only acceptable interpretation of probability?
If not, does someone care to make an explicit argument that the evidential / subjective / Bayesian interpretation of probability is unacceptable to use ever in the context of statements about the past? In everyday terms, does anyone want to argue that you must never say "likely" in the context of study of the past? That one must never qualify propositions about its particulars in a probabilistic way, even if using imprecise probability or ambiguous non-mathematical language to implement the description of such a qualification?
Note that many historians have qualifiers such as "likely" or "plausible" in their texts, suggesting they do think in some approximation of probabilistic terms, so this is something of an uphill battle at first glance.
One easy example of this is to consider propositional logic and its extension, first order logic. Already, first order logic provides different ways of describing arguments in simple propositional logic: for example, the premise P, "Socrates is a man," can be represented by the predicate "is_man(Socrates)" and the premise Q, "all men are mortal," can be represented with a universal quantifier. And while we can see these kinds of equivalences, it's also not hard to imagine someone choosing to use the (less powerful) propositional logic. It is simpler and thus easier to explain your thoughts in for a non-technical audience, for example. And there are many different extensions or even mutually inconsistent versions of logic, so perhaps some of them are counter-intuitive or detract from the message of an argument. (For example, nobody would use a paraconsistent logic unless they wanted to emphasize that they tolerate some contradictions to arrive in their system.)
Likewise, nobody would use probabilistic statements unless they wanted to emphasize that some of the propositions they're describing do not have perfect certainty.
Indeed we may find people even permitting a little higher order, philosophical dissonance in order to reduce the amount of miscommunication regarding their emphasis with regards to the lower order, practical flow of representation of their particular arguments.
For example, it's common for people to recognize that their statements are fallible. What does that mean? Their statements are not logically entailed by their evidence. There is a logical gap between the evidence they have and the statements they are willing to assert as beliefs. For example, there is a logical gap between my evidence "I have a memory of having oatmeal this morning" and my belief "I had oatmeal this morning." The major premise connecting them is something like "I can rely on my memory in these kinds of circumstances," but there's no absolute certainty that the human system of memory never fails. And yet to me it's a bit absurd to imagine that I didn't have oatmeal. The memory makes it seem close enough to a certainty to me, that it would be misleading and introduce noise into the conversation for me to speak of anything less than some kind of rounding error of full certainty regarding my credence here.
For all practical purposes, I would in certain contexts be willing to represent this credence of mine as having probability "1" even though I am fallible. Perhaps this would simplify later considerations for me: should I spend energy entertaining possible timelines where I didn't have oatmeal? I don't think so. And if I am not going to do so, there is a practical argument for representing this credence with 1; it lets me move on and not continually consider the probability space of worlds where I did not have oatmeal. This lowers the cost of the effort to be rational with an entirely acceptable trade-off that I have excluded some possibilities even though my knowledge is fallible. It has the further benefit of being less confusing to other people. If I said something else, I would be drawing attention to the vanishing small and theoretical possibility (from my perspective) that I didn't have oatmeal, which makes me sound a bit like a skeptic rather than someone who claims to have knowledge.
So, yes, I agree with several of the points you have made, Paul (if I understood them):
(1) It is coherent to use credences of 0 and 1, including when using the evidential / subjective interpretation of probability.
(2) A key feature of subjective probability is that it is conditioned on the evidence available and considered when the credence is formed: my credence that I had oatmeal, for example, is based on my memory, while any reader of this post has only my testimony.
(3) There are different systems for describing reasoning under uncertainty (and certainty). There is no one system of description that everyone uses all the time.
These are, I think, matters of clarification.
A key underlying subject of dispute, as I see it, is whether the past (even while undertaking some activity of describing the past called "history") can coherently be described in terms that use the evidential interpretation of probability. I think that it can, but I would welcome an argument that shows that it can't. So far the only valid argument that I have seen here is the idea that we have to be using the frequentist interpretation of probability (if we refer to probability), which would be a successful and sound argument if the premise were true. But I don't agree with the premise. So I have argued against dogmatic frequentism.
And even though this is the only argument with valid logic and no misunderstandings that I have seen here, I am also getting the sense that maybe nobody is explicitly defending this argument. There is a distinct possibility that my defense of the viability of the evidential interpretation of probability may end up a little bit neglected, as if irrelevant, because the premises of the argument being made -- e.g., dogmatic frequentism when it comes to the interpretation of probability -- are not fully understood by those making the argument themselves.
Does anyone want to come to the defense of frequentism as the only acceptable interpretation of probability?
If not, does someone care to make an explicit argument that the evidential / subjective / Bayesian interpretation of probability is unacceptable to use ever in the context of statements about the past? In everyday terms, does anyone want to argue that you must never say "likely" in the context of study of the past? That one must never qualify propositions about its particulars in a probabilistic way, even if using imprecise probability or ambiguous non-mathematical language to implement the description of such a qualification?
Note that many historians have qualifiers such as "likely" or "plausible" in their texts, suggesting they do think in some approximation of probabilistic terms, so this is something of an uphill battle at first glance.
Statistics: Posted by Peter Kirby — Thu Jan 16, 2025 2:59 pm