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Of course these are different fields yet I would wager that many consider morality to be subjective but probability to not be.

What is the correct answer to “Should I save my dog over an adult human being?” The answer seems to be: it depends on your moral framework.

What is the correct answer to “What is the probability that I will get cancer in the next ten years?” The answer seems to be: it depends on your definition of probability. This is not only because probability is often defined based on history which begs the question of how far back in history you look at but also because I am a part of infinitely many classes, and each class will each have different frequencies. For example, I am an adult male, but I am also in my 20s. The rates for cancer for these classes can be wildly different.

If both concepts are then fundamentally subjective, why is the former considered to be objective in many scientific fields?

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  • No. The answer to "is the continuum hypothesis true?" depends on one's philosophy of set theory, it doesn't mean that set theory is subjective. Probability calculus is based on axioms, just like set theory. Its empirical application may well be subjective, every application is to varying degrees. But even then it is more regimented than application of moral principles, and we have no "moral calculus" at all.
    – Conifold
    Mar 6, 2023 at 1:35
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    I haven't seen how sausages are made! People say its pretty ugly. Mar 6, 2023 at 10:00
  • that's quite a bold claim. if there is no "method... of reasoning" about morality, rather than no consensus about how to go about it, then that's not subjectivism, that's intuitionism about all cases (which wouldn't get anyone very far in real life @Conifold
    – user67104
    Aug 4, 2023 at 5:54
  • There's philosophical probability and then there's ... mathematical probability. I see now how philosophy is related to mathematics. Aug 4, 2023 at 10:04
  • @Conifold i think that e.g. at least some emotivists agree there can be no moral reasoning about "basic moral principles", but that's not to say that no (i suppose emotivists don't make "judgments") moral response includes reasoning, either about moral or non-moral facts
    – user67155
    Aug 6, 2023 at 4:52

4 Answers 4

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It depends on what you want the term "objective" to mean (there is more than one definition of it around); also the term "probability" is used in a variety of ways.

A major distinction when it comes to the meaning of probability is between epistemic and aleatory probability (the latter sometimes referred to as "chance"; just to connect this to concepts appearing in other answers, frequentist probabilities are the best known variety of aleatory probabilities, and epistemic probability is often identified with Bayesian probability, even though that's not entirely accurate, as aleatory probability can be handled in a Bayesian way and I've seen epistemic probability concepts that are not based on Bayes' theorem).

Epistemic probability is relative to a state of knowledge, which in particular means that there is no unique objectively true probability for any event, as it always depends on an individual's state of knowledge about it. Epistemic probability comes in so-called subjective and objective varieties, where "objective" can refer to (a) a postulated unique objective relation between any given state of knowledge and the resulting probability and/or (b) to principles that govern probabilities in the absence of specific prior information ((a) in fact requires (b)). Proponents of subjective epistemic probability hold that in most or even all real situations there is an irreducible subjective amount of judgment required in order to arrive at probabilities, and therefore probabilities will depend on the individual in a stronger way than just through their factual knowledge.

Aleatory probability refers to the real events/setups/experiments themselves rather than to the knowledge or judgment of individuals. Aleatory probabilities are therefore objective in the sense that the idea is that they are located in the "world outside" independently of the observing individual. Note however that we cannot make sure that objective aleatory probabilities do indeed exist. Most definitions of them will rely on idealisations, in particular potentially infinite identical repetition of experiments, and defining what it actually means to say that the aleatory probability of event A is 0.7, say, is highly problematic and controversial. Personally (and in line with many statisticians) I'd say that aleatory probabilities are a thought construct, defined within the framework of a probability model, and empirical data can be used to check and potentially falsify the model, which will never be literally true but at best useful ("all models are wrong but some are useful" wrote George Box). We treat them as objective, i.e., existing in the world outside, but they are not objective in the sense of existing in a verifiable manner. (Note though that epistemic probabilities are not unproblematic either; the objectivity of objective epistemic probabilities can be challenged as well, and there are measurement issues also with subjective epistemic probabilities.)

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Nope!

Moral and probability are both objective theories. Objective mean they are above then subject wishes.

Problem that not all people are belonging to the subjective unconscious of the current society.

Probability theory works only in games space, if you have parts of mind out of game you don't need probability definition to action. For example religion has objective-subjective structure too, but probability is not working in beliefs. Trustful persons know what should to be out of probabilities.

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Probability and statistics are not considered objective, see Lies, damned lies and statistics. Probability is used as tool for aiding in decision-making processes. It's neither an objective recipe nor an algorithm with an objective output, that is why you still have to go to the doctor instead of asking a machine learning process what's your disease. It's exactly the same as ethical frameworks (consequentialism, deontology, particularism, etc.) also used to help in decision-making processes but never providing any objective and definitive recipe in any particular scenario.

Also, if by objective you mean that results do not depend on the subject, every probability interpretation not including subjectivity (Bayesian) would be objective. But from the final part of your question it seems you're asking why are probability results considered objectively scientific. They are indeed objective in the process, but heavily dependent on the modelling. And modelling varied greatly among statisticians, just as ethical argumentation varies among philosophers.

And keep in mind that generalist ethics (consequential and deontological) assume there exist universal moral principles which can be defined normatively, they are not particularist, which is what I think you're meaning when saying that morality is subjective. See Moral generalism Vs Moral particularism for more details on the distinction.

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There are two commonly accepted definitions of probability:

  • Frequentist probability: The probability of X happening is the proportion of times that X actually does happen, out of all times when X could have happened. This is an objective fact about the universe, and can't be argued with on the basis of opinion. However, our measurements of this value may have some uncertainty. This uncertainty can (in theory) also be quantified objectively, but this usually requires us to make some assumptions about our measuring process (for example, we may need to assume that our sampling method is unbiased, and it's often hard to prove that this is actually the case).
  • Bayesian probability: The probability of X happening is a measurement of how certain we are of X happening, based on the information available to us. Since different information will be available to different people, this is inherently subjective. However, this does not mean that you can just make up whatever probabilities you like. Your probabilities must be consistent with the evidence and with the Kolmogorov axioms, which also entails that you must use Bayes' theorem to update your probabilities when new information becomes available. Since frequentist probability also obeys those same axioms, all theorems of one kind of probability are also true of the other, but have a different real-world meaning because of the different definitions of "probability."

(Some people think that one of these definitions is the only correct definition. But the term is used with both meanings, so it would be pointless to crown one of those groups "right." We would just have to invent a new word for the other concept anyway.)

Some probabilities may only make sense in one interpretation or the other. For example, "what is the probability that candidate X wins the election?" is obviously asking for a Bayesian probability, as this exact election (with this exact electorate and slate of candidates) will most likely never be run again. On the other hand, questions of statistical significance usually revolve around a slightly convoluted use of frequentist probability (in simple terms, you take a statistical measurement, assume that it was just a fluke and then ask "if this measurement is just a fluke, then what was the probability of getting a measurement at least this extreme?" - if that conditional probability is low enough, then you can reject the "it was just a fluke" explanation as implausible).

To focus on the question you actually asked:

What is the correct answer to “What is the probability that I will get cancer in the next ten years?”

This must be a Bayesian probability. You will not live the next ten years multiple times, so frequentism does not apply. There are ways of reframing this probability to be frequentist. For example, "What is the probability that a person who was [some age, health traits, etc.] ten years ago got cancer since that time?" - this is objectively answerable with actuarial calculations, and makes more sense in the context of frequentism than Bayesianism. If there were no objective answer to questions like this, then insurance companies would not be able to operate at a profit. However, the drawback is that you have to decide which traits should be included in the description.

Some traits are easy to measure (from the perspective of the insurer) and some traits are harder (think of age vs. diet). Some traits are more obviously relevant to cancer risk (think of smoking vs. skydiving). The insurer profits by focusing on traits that are either easy to measure, highly relevant, or both. So their probability is not perfectly applicable to you. But from the insurer's perspective, that's OK, because even though all of their probabilities are slightly inaccurate, in aggregate these errors should tend to cancel out on average, if the insurer has done a good job of picking the most important traits, and so they can still make a profit anyway. In this way, we can see that even this frequentist probability is subjective to a degree, because the insurer must necessarily accept a probability that isn't perfectly applicable to the problem domain. But, again, the insurer is not free to simply make up whatever probabilities it likes, or else it will start to lose money, because there is still an underlying fact of the matter. The insurer is simply accepting a less accurate rendition of that reality for business reasons.

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  • There is also objective Bayesianism, and in fact Bayesian probability computations can also be used in a frequentist setting (Bayes Theorem holds regardless of the interpretation of probability used). On the other hand, the term "commonly accepted" is problematic because a good number of (not only) Bayesians do not accept the frequentist concept of probability, or at least see fundamental problems with it. Mar 6, 2023 at 18:35
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    @ChristianHennig: The obvious response to that, is that a word may have more than one definition. A refusal, on either side, to "accept" a definition is simply pointless. People use the word with that meaning, you can't simply tell them that they are wrong to do so.
    – Kevin
    Mar 6, 2023 at 22:58
  • "you can't simply tell them that they are wrong to do so." And I don't. I just note that there is some more variety and controversy than your answer suggests. Mar 7, 2023 at 0:24

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