# Can we fully expunge the notion of probability from philosophy?

Can one reason about things without involving this concept altogether? Although the answer to this is trivially yes since the theory came about only 400 years ago, my question is moreso whether one loses anything by expunging this concept completely.

Let’s first take the “physical” sense of probability. When we say that the probability of a dice rolling on 1 is 1/6, it seems to imply as if the dice roll is affected by some law. But can this simply be phrased another way without involving this concept at all?

Can one instead say “The dice has equal sides and I see no more reason for it to land on one particular side than another given its geometry.”

This seems to capture the same essence of probability without involving an actual figure and makes more clear the idea that there is no fundamental probabilistic law here when it comes to dice rolls.

“The dice rolled on 1” now seems to just be any other event instead of an event that has a probability of 1/6 which can easily result in the confusion that it could have rolled on another side otherwise. For all other events, we don’t do this. If an event such as “John watched TV at 6:06 PM yesterday at his home” occurs, no one thinks of all the different kinds of events that could have happened instead. More importantly, no one thinks that this event occurred by chance. So then why do this for dice rolls? Dice rolls by the same logic don’t occur by some special process called chance either. There is nothing about a dice roll that is special in the way the laws of physics work around it compared to someone watching TV.

When it comes to other kinds of “non physical” probabilities such as epistemic probabilities in regards to a hypothesis, this is more easily refutable. Any coherent hypothesis about the world is either true or false. Trivially, its “actual” probability must either be 0 or 1. But if it’s 0 or 1, we can simply use words that have described this binary state for centuries: truth and falsity.

Finally, some have argued that subjective probability is needed since we often feel confident in some belief more than another. Again, this can simply be phrased as “I feel more strongly about A than B.” or “If I had to pick between A and B, I would pick A.” No concept of probability needed.

Is this concept needed at all when reasoning about anything? If the goal of philosophy is to seek truth, why use any concept that doesn’t have a basis or seems meaningless in many contexts in reality?

• Good luck reformulating the basic theory of fermions and bosons without reference to statistics and probability! Aug 17, 2023 at 18:17
• The question was about philosophy, not physics. Although here’s an interesting talk by David Deutsch who recommends expunging the notion from physics as a whole since in his view, probability just isn’t an actual process in reality: m.youtube.com/watch?v=wfzSE4Hoxbc Aug 17, 2023 at 18:40
• You said that "any coherent hypothesis about the world is true or false," which is debatable. At any rate, quantum physics involves hypotheses about the world, and then there's the philosophy of quantum physics to consider. Now if Deutsch can reformulate Fermi-Dirac and Bose-Einstein (or anyon/bradyon) statistics without reference to probabilities, more power to him, I suppose. Aug 17, 2023 at 18:43
• See 'Why do certain ways of categorizing make sense more than others? Is this the intuition behind natural kinds?' philosophy.stackexchange.com/questions/95400/… Also' Why is a measured true value “TRUE”?'philosophy.stackexchange.com/questions/81655/… Aug 17, 2023 at 18:49
• "the theory came about only 400 years ago" -- you're talking about the formal mathematics of probability. I'm sure ancient Greek philosophers had some notion of probability, they just didn't express it mathematically. Similar to the way Zeno's paradox shows some notion of infinitessimals long before calculus. Aug 18, 2023 at 14:32

Probability is an extremely useful concept, both within science and within epistemology and there is no good reason to want to expunge it. Most of your complaints about it are based on misunderstandings.

When we say of the roll of a six-sided die that the probability of rolling on 1 is 1/6, we are making a statement about our expectations of the outcome based on incomplete information. Suppose for the sake of argument that the universe was perfectly deterministic and we could get exactly the same result from rolling the die given a precise value for its starting position, the magnitude and direction of the impulse applied to it, etc. Even then it remains the case that if we lack precise knowledge of those values, we would still judge that the probability of the die landing on 1 has a probability of (approximately) 1/6. Not because the die itself has some probabilistic disposition but because of our incomplete information.

Bear in mind that until quantum theory came along, people believed that Newtonian mechanics and Laplacean determinism ruled the universe. It didn't stop people from playing with dice, cards, etc. There is nothing incompatible about combining the fact an event has a definite outcome, or a proposition has a definite truth value, with the fact that our information about it is incomplete. We can even coherently bet on past events. If Arsenal played Liverpool last Saturday but neither of us knows the result, there is no reason why we could not bet on it. Betting implies probabilities, since odds and probabilities are interconvertible. The fact that the outcome of the game is a fixed fact of history is irrelevant. What makes the bet a coherent possibility is that we are proceeding from a state of incomplete information about the result.

The John watching TV example is really not different, it's just more difficult to think of all the possible things that John might be doing or form a theory about them that yields definite numerical probabilities. But difficult is not the same as impossible. If I know someone very well I might be able to say that based on their usual routines it is highly probable that they were watching TV at 6:06. Perhaps because I know that one of their favourite shows was on at that time.

To speak of events happening by chance is a huge misunderstanding. It involves hypostatising 'chance' and treating it as if it were a thing that causes other things. Chance doesn't cause anything. Outside of quantum mechanics, nothing literally happens by chance. To say loosely as we often do that something happened by chance is to say that we do not have an explanation of why it happened. To speak of chance is to speak negatively of a lack of information or a lack of an explanation. Chance is not a thing; it is an elliptical way of talking about our ignorance.

I think this also addresses your point about epistemic probabilities. Statements about the world may be either true or false, but our information concerning those statements is almost invariably incomplete. Incomplete information is typically expressed using probabilities. This is how information theory works. Information theory is probabilistic to the core.

Probabilities as degrees of credence are also useful. It is not enough just to say I prefer A to B. If there are many possibilities with different utilities, then quantifying them is important. This is how decision theory works, and again, decision theory is probabilistic to the core. The most common approach to decision theory involves maximising expected utility, and whatever the limitations of that approach, it works pretty well in many situations to a good approximation.

• The whole of information theory is concerned with mapping incomplete information to a probability. Take a look at the Wikipedia article, or at an introductory textbook such as Cover and Thomas. Decision theory, while it can be done without probability, is mostly done using probabilities and utilities. Probability is fundamentally a way to quantify uncertainty. It is part of the human condition that we are uncertain about pretty much everything, but we still have to live and make decisions. Probability helps with understanding our uncertainty and helps with making good decisions. Aug 18, 2023 at 13:19
• Assigning a figure to a probability is not making a claim about a hypothesis: it is making a statement about our ignorance of it, so there is nothing contradictory. The fact that there are propositions where we have a weak grasp of how to assign a probability does not make the concept useless. As to the probability that John will die, his life insurance company knows ways of putting a number to that. As to the existence of gods, we have no grasp at all. It just means there are some propositions of which the only reasonable thing to say is that we don't know and that's it. Aug 18, 2023 at 13:19
• @thinkingman It absolutely makes sense to talk about the extent and/or confidence of our knowledge. Knowledge is not as black and white as true/false or known/unknown, except in theoretical mathematics. If someone rolls a die out of my sight and asks me to guess what they rolled. I have no way of knowing what it is. But I can be very confident that it is either 1, 2, 3, 4, 5 or 6. Even more so if I inspected the die before rolling. It makes perfect sense to quantify the available information as probability 1/6 each that it is 1, 2, 3, 4, 5 or 6, and probability 0 that it is anything else.
– user67356
Aug 18, 2023 at 14:17
• @thinkingman How confident are you in your knowledge that you are between 1m and 2m tall? How about between 1.70m and 1.80m? How about 1.759m and 1.761m? Do you have any way of knowing whether you are between 1.759312m and 1.759313m tall? Does that mean you cannot know how tall you are, and so you have no length?
– user67357
Aug 18, 2023 at 14:28
• I wouldn't call very useful tools to solve very real problems 'fictions'. If anything, the idea of a 'true state of the world' or some Platonic objective reality is a (pretty useless) fiction. But then we're thoroughly in the realm of opinions.
– user67362
Aug 18, 2023 at 15:51

No, probability is a foundational concept in philosophy. But not only that: it is an essential concept of language. Every sentence about the future is essentially an statement of probability: "he will sleep" essentially means "for what I know from the past, I'm 100% sure he will sleep", and also "the probability that he will sleep is 100%". "Never" means 0%, "often" means around 66% (for me, you might have a different expectation), etc.

1. Philosophy covers essentially two domains: physical or empirical (science) and metaphysical or rational (logic, math, etc.).
2. Mathematics is a tool that help us increasing our chances of survival by allowing not just to describe nature (which implies describing the past), but also to predict the future.
3. Probability is the formal way to know approximately if something will occur. Although there's no probability of 100% in the physical world, a high probability means I can be pretty sure that the sun will raise tomorrow.
4. We want to predict the future with or without probability. In simple words, probability is just the formal expression of our knowledge of the world. Without knowing mathematical probabilities, a kid can predict future facys based on its knowledge of the past.

Can one reason about things without involving this concept altogether? Although the answer to this is trivially yes since the theory came about only 400 years ago, my question is moreso whether one loses anything by expunging this concept completely.

No. Without probability, there's no way to express if a fact in the future might occur.

Check that very sentence: "there's no way to...". I'm essentially stating that the probabilities that X are 0%, so I'm using the logic of probability, even if I'm not using the word, a synonym or the mathematical concept of probability.

When you ask "can one reason about...", you are asking a probability, even if you don't use the term, the word or the mathematical concept of probability.

Let’s first take the “physical” sense of probability. When we say that the probability of a dice rolling on 1 is 1/6, it seems to imply as if the dice roll is affected by some law. But can this simply be phrased another way without involving this concept at all?

"by some law": exactly: the laws of nature. How would you phrase it? "probability is what the gods want"?

This seems to capture the same essence of probability without involving an actual figure and makes more clear the idea that there is no fundamental probabilistic law here when it comes to dice rolls.

Yes, there's no "fundamental probabilistic law". Because the probability is part of math, which is part of metaphysics, that is, a subjective construct.

When it comes to other kinds of “non physical” probabilities such as epistemic probabilities in regards to a hypothesis, this is more easily refutable.

It is non-physical only if the subject assesses his own probabilities (which has no sense: I'm using a tool -the brain- to measure the tool itself... What? Am I trying to predict myself? That would be extremely biased) . Otherwise, it is empirical (I measure the "epistemic probabilities" of others, which I know by means of experience, physical facts, not by metaphysical facts).

Finally, some have argued that subjective probability is needed since we often feel confident in some belief more than another. Again, this can simply be phrased as “I feel more strongly about A than B.” or “If I had to pick between A and B, I would pick A.” No concept of probability needed.

False, you are predicting/describing the world. You are using the logic of probability, just without the maths of probability.

Is this concept needed at all when reasoning about anything? If the goal of philosophy is to seek truth, ...

It is necessary. Truth has not only a physical (empirical) component, but also a metaphysical (rational) one.

Remember that truth is subjective. Your truth (the probabilities you expect) is not the same as my truth (those I expect).

• You are assuming the conclusion in your premise. Saying that every statement about the future is a probability statement assumes that a probability statement is meaningful. But in what sense does John sleeping tomorrow have a 100% chance? Maybe he’ll stay up and do an all nighter with a Red Bull. What is the real chance then? 99%? 97%? Hell, why is even 3% wrong? Maybe knowing that he has strong anxiety that day will make you think he won’t sleep. There is no correct answer to this. But if there is none, why use this concept in the first place? It’s nothingness measuring nothingness Aug 18, 2023 at 10:45
• "Every sentence about the future is a statement of probability" is completely false. It is not the case that we require any notion of probability, even a naive one, to deal with events that are uncertain. There are some phenomena (like the double slit experiment) which nobody has a good explanation for without using probability. But the idea that a numerical theory of uncertainty is required to deal with uncertain statements at all is absurd. Aug 19, 2023 at 6:57
• @preferred_anon No problem if you disagree, but ask yourself if you will go to the cinema next monday. You know your answer. Even without the concept of probability, you are still using the logic of probability. If you are completely sure that you will not go to the cinema, you can express it in words. Or in terms of `Probability(me going to the cinema) = x`, where `0 ≤ x ≤ 1`. Aug 19, 2023 at 19:01

You are right to protest at the casual use of "by chance" that treats chance as some kind of quasi-cause and to insist that probability is a substitute for accurate and complete knowledge. But that does involve assuming that Determinism and the Law of Excluded Middle are both true. However, neither of those is unquestionable, as I'm sure you are aware.

You don't mention the obvious difficult case for your argument - Quantum Mechanics, so I assume that you know that the question whether probability is embedded in reality is still contested. See Stack Exchange - Determinism & Quantum Physics)

Your discussion of what you call "other kinds of “non physical” probabilities such as epistemic probabilities in regards to a hypothesis, this is more easily refutable. Any coherent hypothesis about the world is either true or false."

The last sentence of that quotation is not exactly true and not exactly false - it is over-simplified. Hypotheses can be plausible and implausible, accurate or inaccurate, exaggerated or minimized, distorted or not and so on. So, for example, Newtonian mechanics is not refuted by Relativity Theory; it is just that it is inaccurate under certain circumstances.

For a use of probability beyond physics and logic, you may like to consider the legal concept of probable cause and whether that should be eliminated. "In the context of warrants, the Oxford Companion to American Law defines probable cause as 'information sufficient to warrant a prudent person's belief that the wanted individual had committed a crime (for an arrest warrant) or that evidence of a crime or contraband would be found in a search (for a search warrant)'." Wikipedia - Probable cause

There are more humdrum, but still important uses for probability. It is true, and annoying, that probability cannot help us more than marginally in deciding what to do, but it is very helpful in enabling us to decide, for example whether to take a raincoat with us when we go out or whether to take out life or travel insurance. And then there is always the human fondness for gambling and I don't suppose that any pruning of human language will eliminate that.

I would suggest that it is more plausible to explain probability as enabling us to extract some knowledge from situations in which the knowledge available to us is limited. The concept assumes that a probability can be replaced by an outcome, so it does not necessarily undermine either determinism or the law of excluded middle (saving, as always in these discussions, the interpretation of quantum mechanics.)

• Detailed answer but I do want to make a quip that I wasn’t merely focusing on just the fact that chance may not exist as a process, but rather that we see various events as chancy (such as dice rolls) and other events as non chancy (such as me sipping my coffee). Whether determinism is true or false, it makes no sense to think of these events as stemming from different processes Aug 17, 2023 at 21:52
• I don't disagree with you. I think I would rather say that whether we see a given event as chancy or caused depends on the context in which we place them - in one case in the context of incomplete knowledge and in the other of complete (or at least adequate) knowledge. Would you disagree with that? Aug 18, 2023 at 3:39
• @thinkingman Dice rolls and sipping coffee are different in degree, not kind. There's uncertainty involved in coffee sipping (scalding yourself; "going down the wrong tube"; having absentmindedly finished it 5 minutes ago; being poisoned by a jealous coworker; etc.). It's just that - in contrast to dice rolls - the probability of those events are so low as to be negligible in most cases. (Though John is abnormally interested on how I'm liking my coffee this morning ...)
– R.M.
Aug 18, 2023 at 12:11

Your premise that there is no difference between the TV-watching statement and the die roll is false. To start with, either John was watching TV at a certain time or he wasn't when we looked (two different outcomes) or the die landed on (1, 2, 3, 4, 5, or 6) when we looked- six different outcomes.

Your conclusion that probability doesn't have a basis or is meaningless in many contexts in reality is false as well. It has a basis in any context where a single cause can result in a distribution of different outcomes, and possesses a rigorous mathematical foundation.

As to whether there is a need to include or exclude statistics and probability from the practice of philosophy is for the philosopher to decide, because unlike mathematics (which is based on rules), philosophy is based on whatever you want to think.

• Not true. You can come up with any number of outcomes in the John scenario. For example, he could have been watching TV with his fingers resting on his jaw, with his legs crossed, with his cat on his legs, etc etc ad infinitum. The sample space is a function of how you want to describe events, not something that is inherent to the event itself. Aug 17, 2023 at 18:33
• As for the meaningless talk, I argued that it is meaningless in the case of epistemic and subjective probabilities. In the case of physical probabilities, it is not meaningless but rather unneeded since it often comes with the additional assumption that a certain process is happening “by chance”. Chance doesn’t exist. Aug 17, 2023 at 18:35
• As a non-physicist, try to imagine "chance" as "accident". Every time you drive your car, you are at risk of an accident. That risk level can be quantified statistically. When you say that chance does not exist, what exactly do you mean? that accidents do not exist? or that statistics does not exist? Aug 18, 2023 at 1:56

Given the connection between quantum logic and probability theory, then among other things, one would have to deal with Bell's theorem and the Kochen-Specker theorem in some way (interpretations of the theorems may vary).

Granted, our knowledge of logic and mathematics, or physics, is not yet absolutely absolute. So there seems (ironically or paradoxically) to be some chance that we might disprove the theory of objective chances after all. But perhaps this would go to show that the concept of probability is inescapable in that, by speaking of meta-probabilities, and being able to speak of meta-meta-probabilities, etc., we know mathematically a priori that the concept has infinite significance. One might argue, for example, that conceptually distinguishing chance from randomness authenticates the structural reality of the concept of chance per se.

Qualification: another issue arises if macroscopic indeterminism exists via something like "the ability to do otherwise." (Whether such an ability is required for moral responsibility is in dispute, but for the time being we will ask about the world just in case the ability exists, regardless of whether this existence is needed for some other purpose.) Presumably, at any given time, it would be possible for us to select from among only finitely-many options, though we might be able to choose from infinitely many when adopting an eternal standpoint.

Either way, it would seem possible to assign a partial probability to any possible such choice, so let's use the (seemingly) simplest possible case, one where we can choose to act or to not act at all. Again, assuming the ability-to-do-otherwise strictly enough, this will not mean that "for all we know," there is a 50% chance that we will act and a 50% change that we won't act; it's just directly 50/50 whether we will act. If we have two substantive options on top of the null one, it might then be that there's a 1-out-of-3 chance that we'll do the one thing, 1/3 the other, and 1/3 nothing; and so on.

Now, it might be possible to reformulate our expectations based on the idea that the will feels pressure to exercise itself in certain ways, so that amounts or degrees of pressure affect the probabilities. Suppose we have a set of desires (A, B) and A > B. Start by assuming that, if it were not for the ability-to-do-otherwise, we would 100% be given over to A. Then we might calculate the fully actual probability of A modulo the ability-to-do-otherwise as ((100% + 33.33...%) / 2 = ~67%). I am treating B as a substantive option, so its initial probability otherwise is 1/3 (alongside a 1/3 chance of total inaction), but per the strength-of-desire factor its probability is 0%. So then we get an approximately 16.67% chance that we'll act on B. I suppose the probability of inaction would be 0% at most, here, but maybe relative to the desire-factor it would actually have a negative probability just in case our only actual desires are for A and B and there is no C-desire to be inactive (no desire-to-do-nothing). Then we'd reformulate the final probability of inaction as (-x + 1/3)/2 = (-3x + 1)/6, or then there'd still be a negative probability of inaction (albeit a lesser negative probability). Something about unitarity rules this out in normal probability theory, but I would be surprised if the probability theory of an ability-to-do-otherwise would have to entirely conform to normal such principles.

Other philosophical considerations: we also want to retain the option of appealing to objective probabilities in moral reasoning. In A Theory of Justice, §28, Rawls contends "that judgments of probability must have some objective basis in the known facts about society if they are to be rational grounds of decision in the special situation of the original position." Generally-speaking, in §4 of the SEP article on interpretations of probability, Hájek surmises that:

It should be clear from the foregoing that there is still much work to be done regarding the interpretations of probability. Each interpretation that we have canvassed seems to capture some crucial insight into a concept of it, yet falls short of doing complete justice to this concept. Perhaps the full story about probability is something of a patchwork, with partially overlapping pieces and principles about how they ought to relate. In that sense, the above interpretations might be regarded as complementary, although to be sure each may need some further refinement. My bet, for what it is worth, is that we will retain the distinct notions of physical logical/evidential, and subjective probability, with a rich tapestry of connections between them.

Probability is fundamental to human thought, and if one takes the metaphilosophical position that philosophy has the aim of using language to clarify thought, then probability inheres to philosophy in the same way arithmetic inheres to mathematics.

Metaphysics for instance examines the notions of contingent truth. Contingency is inherently uncertainty in logical consequence, and therefore discussing the world means that it's useful to consider which world we are discussing exactly. Hence, we have possible worlds.

Another example is the notion of induction, which is a major category of logical consequence, one in which conclusions are uncertain. Uncertain conclusions are amenable to probabilistic analysis. Therefore informal logic which is governed primarily by inference to best explanation and induction is predicated upon probability.

Is this concept needed at all when reasoning about anything? If the goal of philosophy is to seek truth, why use any concept that doesn’t have a basis or seems meaningless in many contexts in reality?

So, yes, almost all reason is probabilistic, and most truth and most realities are not certain, but are based on best guesses and ambiguities. Probability is fundamental to philosophy.

• Similar to the other comment, I think you’re also assuming the conclusion in your premise. When you talk about concepts like certainty, and reason being probabilistic, you must first define what these mean. And the more you delve deep into this, the more you’ll realize you can’t in an objective sense. What is the probability that the moon is really made of cheese? Aug 18, 2023 at 10:51
• @thinkingman the more you analyze the concept of objectivity itself, the more you'll realize how vaporous it is. Everything you know, you know subjectively; if you're not conscious of it to some slight extent, even in memory, you don't know it. So since everything is partly subjective, and all abstract concepts are debated, what do you do? If you have a sense of prosociality, you try to find common ground with others, not dictate to them what is "rational" (as you analyze the word "rational," you'll find that it can be "vacuous" also). Aug 18, 2023 at 13:30
• I for the most part agree. The difference is that we KNOW that there are certain answers to things even if we can’t find them. It is a logically necessary fact that the world either is or isn’t a simulation. There IS a right answer even if one can’t have absolute knowledge. In the case of probability, there is no right answer. It is merely a measure of arguably nothing. “Uncertainty” doesn’t exist in a real sense in the world. Weight on the other hand, for example, is a measure of something real and physical. Aug 18, 2023 at 13:36
• "What is the probability the moon is really made of cheese?" This is nonsensical. See Colorless green ideas sleep furiously. As for presuming the conclusion, you confuse the map for the territory. The language of probability is what we use to communicate about the experience of probability. Brains have been computing probability intuitively long before language evolved. Chimps can be uncertain and decide. No words are needed.
– J D
Aug 18, 2023 at 14:36

"More importantly, no one thinks that this event occurred by chance. So then why do this for dice rolls?"

John watching tv is a choice = John decides to watch tv.

• Non-mathematical probability for John watching tv can be estimated, if you have knowledge about John's prior behaviour
• Choice is a causal factor, John's choice causes him to watch tv

A die rolling to a specific result happens by chance = No-one decides which way the die lands.

• Mathematical probability for this can be calculated by analyzing the geometry of the die
• Chance is a non-causal factor, the rolling of the die is caused by the player's choice to throw. The result is due to probabilistic inaccuracy in the process.
• Choice is merely a mental event which is merely a chemical reaction which itself depends upon earlier factors. He physical laws operating here are the same Aug 18, 2023 at 4:49
• @thinkingman Mental events are not physical events. Choices are made for mental reasons, not due to physical causes. Aug 18, 2023 at 4:57
• What? So you think they happen out of a vaccuum? Aug 18, 2023 at 6:21
• Each mental event may be a property of a physical process in the brain, but that physical process will have a preceding physical cause within the brain. By extension, the mental event has a physical cause Aug 18, 2023 at 11:01
• It doesn’t matter if they are different. Being different from physical processes does not imply they weren’t caused by physical processes Aug 18, 2023 at 11:55

Can one fully expunge predicate logic from philosophy?

Can one reason about things without involving this concept altogether? Although the answer to this is trivially yes since the theory came about only 134 years ago, my question is moreso whether one loses anything by expunging this concept completely.

Let’s first take the “physical” sense of predicate logic. When we say that the truth value of 'all men are mortal', it seems to imply as if the statement is affected by some law. But can this simply be phrased another way without involving this concept at all?

Can one instead say "Men are living beings and I see no reason for them to live forever."

This seems to capture the same essence of predicate logic without involving an actual inference and makes more clear the idea that there is no fundamental logical law here when it comes to dice syllogisms.

• Of course you can talk and even think about things without invoking additional concepts. You may be implicitly using the concepts, but you can still talk and think about them. But that seems not to be what you meant.
• Just because a formalism has or hasn't been invented and named and studied a lot, doesn't mean that you can't use and think in a manner consistent with the formalism. We can talk all day about Mars and Saturn and even the concept of planet without caring about Uranus, whose existence was denied. But that seems to be not what you meant.
• Probability is a formalism to capture uncertainty. While most examples of probability are discussed in the language of mathematics, which tends not to be the desirable in the language of philosophy, probability is a way of making statements about uncertainty that are less vague than without that language. But that seems to be not what you meant.

What you seem to be suggesting, by the way you ask the question, is that philosophy doesn't need the formalism of mathematical probability. You could just as easily say the same thing about predicate logic - the great majority of epistemology and ontology can be discussed without invoking the formalisms of either probability or predicate logic. On the other hand, logic and uncertainty most definitely are central to (much of) philosophy.

In terms of quantum mechanics: Unitary time evolution is perfectly deterministic. Collapse on "observation" is probabilistic in accordance with the Born rule, but not all QM interpretations have this. For example, Everett's relative-state formulation has no observers or collapse, meaning the evolution of the Universe's wave function remains deterministic. So at this level I'd say the answer is yes - there are formulations that don't require probability as a "real" physical property.

But if it’s 0 or 1, we can simply use words that have described this binary state for centuries: truth and falsity.

Counter-intuitively, events with "0% probability" can still happen and events with "100% probability" can still fail to happen. Consider throwing a dart at a continuous dart-board - it'll hit somewhere despite having had 0% probability of hitting that exact spot and 100% probability of hitting anywhere but there.

Probability on its own can only make other statements about probability. A coin having 50-50 odds implies that if you flip it 10 times you're "more likely" to get 5 heads and 5 tails than other outcomes, but not that you actually will. To ground it in reality, we have axioms about how rational actors should behave given certain probabilities, options, and outcomes. I don't see any particular reason why you couldn't instead describe how a rational actor should behave in terms of some other measure of credence (though I think a lot will follow from very few uncontroversial assumptions, and you'll end up back at something similar to probability).

Let’s first take the “physical” sense of probability. When we say that the probability of a dice rolling on 1 is 1/6, it seems to imply as if the dice roll is affected by some law. But can this simply be phrased another way without involving this concept at all?

Sure can. It means that in the past you rolled the dice, or a similar dice, a large number of times, and we got 1 pip about 1/6 th of the time. This is just simple counting and can be explained without any notion of chance or uncertainty.

I want to speak to the questions about the meaningfulness of probabilistic statements.

I think the OP's opposition (as mostly refined in their responses to subsequent posts) to using the formalisms of probability stems from their position that declarations of probability are fundamentally flawed. I think this is an important piece of discussion to clarify because it seems like a sentiment that feels rather reasonable if one considers the common approaches to teaching elementary probability theory in many books and classrooms.

First, while there could be other times we use probability statements, some cases include: to describe predictions, to describe knowledge, or to describe mathematical systems. In fact, all statements of probability really boil down to statements about mathematical systems—that is, systems where complete knowledge about the possibility space is defined.

I think an underlying problem many creative students may have with studying probability theory is with defining the possibility space. To define the space of all possibilities requires a combination of shared conventions in linguistic interpretation, shared conventions on logical operations, and perhaps most importantly shared knowledge of everyday experience.

So let's consider, the prediction that I will roll a 1 on a "fair six-sided" die. I could formalize an estimate of the likelihood of rolling a 1 by considering a mathematical system consisting of a "space" equally partitioned into six mutually exclusive possibilities: "rolling a 1", "rolling a 2", ... and lastly "rolling a 6". This mathematical system can be used to assign a probability of 1/6 to rolling a 1 on a real world "fair six-sided" die only if we accept the following:

• the six possibilities of the mathematical system model the physical possibilities of what we mean when we describe something as a "six sided die rolling to a particular outcome"
• we agree that a declaration of a "fair die" means that using either data or hunches about the bias of a die allows us to assign equal "weight" to each of the 6 mathematical possibilities.
• other physical possibilities (like a fish flying out of the air eating the die before it lands, or a die that is able to balance on an edge, or a die slightly leaning between the "1" side and the "2" side) are considered negligible given both our shared experience and a shared commitment to accepting the Law of the Excluded Middle.

When we agree to all of the above, there is a fact of the matter about what the correct probability of the prediction is.

But, we can also use similar agreements to describe our knowledge concerning the proposition that "the die on the table just rolled a 1". (Notice the past tense.)

• we have to agree to what it linguistically means for a die to roll a particular outcome (here the possibility space could admit alternative linguistic possibilities relevant for modeling our knowledge of the proposition)
• we have to agree that other physical possibilities beyond "rolling an X" are negligible (like the possibility that a magician stole the die that was being rolled and shone light into our eyes by which it appeared that the stolen die was actually sitting on the table looking like it was rolled to a 1).
• for each (linguistic or physical) possibility that we do not want to dismiss as negligible, we can attempt to agree on data or hunches to support assigning weights to each possibility.

Thing is for the above scenario about knowing that
"the die on the table just rolled a 1". We may commonly describe all other physical possibilities as negligible so there is just one physical possibility in the space of all possibilities in the mathematical system modeling our knowledge. In such a case we may assign a probability of 1 to the evaluation of knowledge of the proposition. This may commonly be considered the "correct answer" for many everyday probabilistic statements regarding knowledge, but sometimes it is harder to agree on what alternative possibilities are negligible (see Gettier problems of epistemology). Such difficulties plague all assertions of knowledge not just probabilistic ones.

Our knowledge of the event is different from the facts of the matter regarding whether it is true that the die on the table just rolled a 1. Others have commented about what linguistic and logical agreements and which facts about physics are required to say the fact should either be true or false. But, even if physical facts like this were always just true or false, we might still be tempted to use the statement that the event "had a probability of 1/6" only because we are returning to what statements could be said of the mathematical system that models this kind of die throwing.

Mathematical models of a variety of human behavior, like some person's early evening entertainment activities, are more difficult to define/agree upon the possibility space for. So, using probability theory to describe predictions for human behavior is murkier. However, modeling our knowledge that "John watched TV at 6:06 PM yesterday at his home" may feel to many the same level of difficulty with modeling knowledge of "the die on the table just rolled a 1". Nevertheless, because of the difficulty in modeling the prediction about John's behavior, it is not likely that people will be trying to describe the event regarding John's TV watching by using probability statements regarding a mathematical system defined around predicting John's early evening entertainment activities.

To wrap up here, the thing is: meaning is inherent in human shared understanding. To define the possibility space of a mathematical probabilistic system is to commit to a variety of agreements about linguistics, logic, and human experience. It is a human construct. If you wish to deny the "reality" of human constructs like the price of water or whether it is no longer fashionable to wear a codpiece, you can but everyone else is going to look at you strangely because you are missing a piece of shared human reality. Alternatively, keep in mind that things that you may take to have more "bearing on reality" like physical measurements of distance or voltage are also caught up in constructs like the units of measurement and measurement protocols that we humans agree upon.

If the goal of philosophy is to seek truth, why use any concept that doesn’t have a basis or seems meaningless in many contexts in reality?

The manic tendency of 20th century Anglo-Saxon philosophers to "expunge concepts" is so passé. Concepts are tools. If you don't like wrenches, you are welcome to not use wrenches, but I will keep using them, thank you very much.

If you don't understand a concept, find it vague or don't believe in the existence of what it tries to represent, then don't use it yourself, but let others use it if they want to.

There is no rational reason to suppress a concept, other than a lack of tolerance or appreciation for what the concept implies.

Here the phobia is probably (:-)) about the undeterminism of life, the fact that shit happens in an unexpected way. An irrational fear of chance, is what I see at the bottom of this question.