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We refer to things being possible when we imagine a class of events that don’t break certain laws.

But this class is clearly mind dependent. For example, could world war 2 have started on a different date? Sure, one can imagine this event, but how do we know this to be possible if a) it didn’t happen and b) we have no way of showing that it could have happened otherwise?

World war 2 happening on a different date seems more “possible” than me jumping off a cliff and flying. But is it really? It seems to be so only because we put the second event into the class “people flying”, match it with our inductive experience of seeing no people fly, and then call it impossible. However, one could theoretically put this event in the class “animals flying”, notice that other animals have flown, and then call it possible. This seems unintuitive but I can’t think of a reason to suggest it shouldn’t be classed like this apart from practical use.

Similarly, one can put the world war event in the class of “wars starting on some day”. Now, in our experience, we have seen wars starting on other days. Thus, world war 2 starting on another day seems “possible.” However, one can also class this as an event of type “world war 2 starting on a particular day.” Now, we don’t have any inductive past experience of world war 2 starting on a different day: we have a sample size of one. When classed this way, there is no way to suggest that world war 2 starting on another day was possible.

There seems to be no mind independent reason to prefer one class over the other. If so, does this mean the notion of possibility and impossibility is merely nothing but a human exercise and not actually fundamental to reality?

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    Yes, there are events which did not happen but were possible: Consider the decay of a single radioactive atom at time t. It could also decay at a different time.
    – Jo Wehler
    Feb 27 at 6:17
  • @JoWehler How do you know? Feb 27 at 6:20
  • It is a result from the quantum theory of radioactive decay: The single event on the microscale is undetermined.
    – Jo Wehler
    Feb 27 at 6:26
  • 1
    According to quantum theory the single event on a microscale is undetermined, which is more than unpredictable.
    – Jo Wehler
    Feb 27 at 6:33
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    Baby, I was about to ask for clarification of some of your more important words or phrases but it seems far too many rely more on personal interpretation than received wisdom. The more so from the way you go on to use them, it seems to me by no means obvious that you give the same meaning as anyone else to even half the words in your first sentence: refer/things/belong/possible/imagine/class/event/break/law… never mind going on to clearly/mind/dependent. Feb 28 at 18:12

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Why do I get the feeling of deja vu? Your question is simply about the meaning of words. When we say something is possible, we mean that we can't think of plausible reasons why it wouldn't be. If it is predetermined that I will wear my pink hippo socks today, then it isn't possible that I will wear my yellow bicycle socks. However, I don't know that my choice of footwear is predetermined, and I can't think of any other reason why I might not wear my yellow bicycle socks, so I say that it is possible that I might wear them.

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According to the IEP article on quantum logic:

According to Werner Heisenberg, the concept of the probability wave “was a quantitative version of the old concept of ‘potentia’ in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.” [152, p. 42] Indeed, contrary to classical possibility which only refers to our incomplete knowledge of an actual state of affairs, quantum possibilities interact between each other. This fact, completely foreign to classical theories, is exploited by present technological developments in quantum information processing for example, quantum computation, quantum cryptography, quantum teleportation.

Or as they say even more directly a little bit earlier:

“In classical physics the most fundamental description of a physical system (a point in phase space) reflects only the actual, and nothing that is merely possible. It is true that sometimes states involving probabilities occur in classical physics: think of the probability distributions ρ in statistical mechanics. But the occurrence of possibilities in such cases merely reflects our ignorance about what is actual. The statistical states do not correspond to features of the actual system, but quantify our lack of knowledge of those actual features.” [98, p. 124-125] In QM however, the different structure of the physical properties of the system determines a change of nature regarding the meaning of possibility and potentiality. Indeed, QM has been related to modality since 1926 when Max Born interpreted the quantum wave function Ψ in terms of a density of probability. However, it was clear from the very beginning that this new quantum possibility was something completely different from that considered in classical theories.

The concept of possibility is simple and subtle enough to not really be definable entirely in terms of other concepts. Note that, on the axiomatic approach, we "lay down rules" governing the possibility operator or predicate or whatever, and proceed from there. We would know that something is possible relative to the given axioms. Per the above, quantum physics appears to be an empirically strong theory whose guiding logic has a place for a notion of possibility, but you should be minded to ask whether their use of the word "possibility" is the same as yours. Kant at one point laments:

Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception—the condition of which is that it be not self-contradictory, for the transcendental possibility of things—the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.

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There are a few possible ways in which "possible" (including "possible worlds") can or seems to be used:

  1. Roughly anything that's conceivable. This would just exclude self-contradictory or inconceivable things like square circles (but maybe someone would argue it's conceivable for a universe to exist where self-contradiction is not a thing, although I'm not sold on that idea).

  2. Something that could've been true in this universe (presuming indeterminancy) had random events been different or (if libertarian free will is true) had different choices been made by people or deities (if one or more exist) or other beings with free will.

  3. Something that can be true given our current understanding of reality. If you flip a coin and look away as it lands, you can say it's possible that it landed on heads or tails. If you look at it and see it landed on tails, it's no longer possible that it landed on heads (or your perception of the coin is not accurate).

    We have a limited understanding of reality and where things could've been different (if anywhere). So that somewhat blurs the lines between these first 3 points, as well as the last point. Unlike this point, the other points allow for things that aren't true about this universe, although there aren't that many things that are conceivable which we can say definitely cannot be true about this reality (unless you combine a bunch of facts that include our perception).

  4. One world within a sort of multiverse where all possible worlds actually exist. The main place I've seen this in philosophical discourse is in Plantiga and Craig's versions of the ontological argument, where it seems to be that this definition is used, but it fallaciously equivocates with one of the other definitions (or it just defines God to exist) by doing something like "God is possible (conceivable) and if God exists in one possible world, then God must exist in all worlds, so God exists".

    The multiverse idea is also commonly used in science fiction and in one interpretation of quantum mechanics.

"Possible" could of course also refer to future events, which would mostly relate to the last 2 points (although, again, the lines are blurry).

Colloquially speaking, the distinction between these may not be that important. But if someone wants to use "possible" in a logical argument (particularly in a way that relies heavily on the definition of "possible"), one should carefully consider and define what exactly is meant.

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This question seems to have been spawned out of a discussion that Baby Philosopher and I had about "metaphysical necessity", and whether it limits the contingency of our world. Here is the link: https://chat.stackexchange.com/rooms/151712/discussion-between-dcleve-and-baby-philosopher.

What we know is that there is no "logical necessity" that constrains physics from being contingent.

Baby Philosopher is postulating there is some kind of "metaphysical necessity," which isn't a logical necessity, but I was unable to get clarity from him on what that "metaphysical necessity" might consist of, or how it might act. Without clarity on the proposed claim, nor evidence to support it, I offered that there is no reason to accept a "metaphysical necessity".

We also know that there are no "laws" of physics that constrain physics. Per this PNAS article, the symmetries that spawn apparent "laws" are all spontaneously broken, which means that all laws are only regularities. https://www.pnas.org/doi/10.1073/pnas.93.25.14256#:~:text=A%20more%20important%20implication%20of,independent%20quantity%3A%20a%20conserved%20charge. So physics has discovered that it does not operate under an "unbroken law" structure that is a prerequisite for an even only "effective" determinism.

We also know that quantum mechanics is probabilistic/indeterminate as the Heisenberg uncertainty principle leaves the location, energy, etc. of particles intrinsically not nailed down. And given chaos phenomena, the Heisenberg Uncertainty can leverage up to macro scale events. So, given human social behavior is almost certainty a chaotic phenomena, "YES, WW2 could have happened at a different time."

I offer a further comment on Baby Philosophers reasoning methodology. He is postulating the spectrum of all possible ways the world could be, then holding that any of them are equally likely if we have no definitive refutations of them. This logic based approach is how most AI used to address possibilities. There is an excellent discussion of how this approach quickly leads to effectively infinite option explosion, and resulting inability to reach any useful conclusions in the world, in this excellent work on the historical failures of AI and consciousness: https://www.amazon.com/Shadow-Consciousness-Little-Less-Wrong/dp/1507869177

The issue that Baby Philosopher and these AI coders encountered is the consequence of applying the Quine-Duhem thesis to decision making. One can identify an infinity of different theories that are compatible with an observation. Empiricism, to be useful, has to narrow that infinity down based on some criteria other than logical possibility. Empiricism basically only considers options that are already established as being at least plausible based on simplicity, coherence and utility. AI has great difficulty making these pragmatic evaluations, and the recent success of Chat GPT etc. has only come thru AI “borrowing” the sum of OUR judgements.

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  • I am not postulating a metaphysical necessity and in no comment have I ever said that. Please don’t put words in my mouth. I was asking you for evidence behind physical contingency, not logical contingency. When we think of possible things, we don’t just think of logically possible things. We refer to things that are physically possible that may have not happened but not logically impossible. Some things are considered physically impossible but not logically impossible Feb 28 at 2:50
  • @Baby_philosopher — contingency is a logic category, just as necessity is. If you want to postulate another type of necessity and contingency in addition to these logic terms, you really have to articulate what these other concepts are. The other people who have tried to do so have used the term metaphysical necessity. I don’t think any of them have made any sense. But with your lack of success as well, you should probably look up some of those efforts, and knowing the term to research would make your research easier.
    – Dcleve
    Feb 28 at 3:05
  • The question is about what’s considered possible. It isn’t about logical contingency Feb 28 at 4:52
  • @Baby_philosopher -- Science operates off logical contingency. I spelled out why in this answer. Your effort to ascribe some other form of necessity to science is contrary to science.
    – Dcleve
    Feb 28 at 6:15
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In the broadest sense of the word, "possible" means "possible according to the laws of nature". Or, of you want, possible according to our understanding of how our reality works.1

Now, it should also be noted that our understanding is always individual -- each person has their own. However, since we all share the same objective reality,2 the individual understandings of how it works should also agree. This common understanding is often referred to as "knowledge".

1 For example, the asteroid missing our planet 70 million years ago, and humans evolving directly from dinosaurs with more efficient avian brains -- that was a real possibility. But the Middle Earth with elves and magic is not -- in other words, the latter is pure fantasy.

2 At least according to science -- or, rather, science itself is based on the assumption of one and only objective reality. This reality is also assumed to be deterministic -- and it is the fixed laws of nature that determine how causes create their effects.

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It depends on your metatheoretical views. A modal realist believes not only is anything that is conceivable possible, but that it is actually occurring by virtue of its possibility. This conceivability criterion is an important element to a theory on modality. The SEPs Epistemology of Modality is a good introduction into the nature of possibility. From the article:

the epistemology of modality seeks to provide answers to the following question... General question: How can we come to know, or be justified in believing, what is necessary, possible, contingent, essential, and accidental?

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We refer to things being possible when we imagine a class of events that don’t break certain laws.

Those "laws" are already a scientific notion, philosophically I think we should go back to Aristotle and his distinction potentiality vs actuality: see e.g. Potentiality and actuality on Wikipedia.

But I think your statement does capture the idea that the notion of potentiality indeed is not simply that "anything that has not (yet) happened can happen", there must be already an intrinsic possibility that it happens: similarly, for an analogy, to potential energy, which is not just absence of energy; or, for example, as in Murphy's Law, which does not say that "anything (that has not yet gone wrong) will go wrong", it rather says that "anything that can go wrong will go wrong".

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If you define "possible" more precisely and make statements in an unambiguous manner, the issues go away.

You say, "We refer to things being possible when we imagine a class of events that don’t break certain laws". We can define this more formally by stating that an event is defined to be possible if and only if it does not have a probability of 0 given a set of statements that we've already accepted as true1, and that we accept some set of statements (such as the laws of physics) as axiomatically true before we start. (Although in practice, we probably consider something impossible if its probability is below some threshold ε where it'll never happen in practice. This is fine, as long as we're clear that by "impossible", we mean "impossible for all intents and purposes".)

[A human jumping off a cliff and flying] seems to be [impossible] only because we put the second event into the class “people flying”, match it with our inductive experience of seeing no people fly, and then call it impossible. However, one could theoretically put this event in the class “animals flying”, notice that other animals have flown, and then call it possible.

There exist sets "humans" and "animals". "humans" is a proper subset of "animals". It is true that "There exists some A in animals such that it is possible for A to fly without mechanical assistance". It is not true that "For all A in animals, ...", nor is it true that "There exists A in humans s.t. ...". If we say, "If A is in animals, it is possible that A can fly unaided"; it's informal shorthand for "there exists some value of A such that the statement is true, given the laws of physics as currently known."

Thus, world war 2 starting on another day seems “possible."

Before WWII started, it was possible for it to start on a different date. It is not currently possible for WWII to have started on a different date (assuming time travel is impossible). If we say "It's possible that WWII could have started on a different day", it's informal shorthand for the first one.

If you want unambiguous statements, colloquial English isn't going to give you that. If you're having a casual conversation, you can speak normally and people will intuit what you actually mean (more or less. usually.), and your sentences will be reasonably short. But if you're going to be doing more heavy philosophy, you need to start talking like a mathematician.2


1 Proper zero probability. Not zero in the limit like the probability that we uniformly select a real number in [0,1] and get 0.5. Zero like the probability that we uniformly select a real number in [0,1] and get 42. I really wish we had language for succinctly stating which of those we mean.

2 That's informal shorthand for "the probability that a sentence will admit an interpretation that is inconsistent with your intended meaning is significantly higher if you speak in colloquial English than if you speak using mathematical formalisms."

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Can anything that doesn’t happen really be “possible”?

Something that has never happened over the lifetime of the universe has a current probability of zero.

But the universe is constantly getting older. An event that has never happened (so far) may happen in the next 1000 years.

So the current probability is zero but it's a time-dependent probability with no guarantee that it will remain zero. The uncertainty is unknown. So anything is possible.

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Schrodinger's Cat

SOURCE:https://en.wikipedia.org/wiki/File:Schrodingers_cat.svg

What you are describing is the foundation of the Schrodinger's Cat thought experiment. To explain the principle of uncertainty in statistics, Schrodinger posited that if you put a cat into a box that you cant see into, and insert a thing that may or may not kill the cat, then it is possible that the cat is either alive or dead.

Possibility in this context is another way of saying that there is uncertainty. As long as you don't look in the box, the cat could possibly be in either state. But, once you open the box and make an observation, it becomes certain that the cat is either alive or dead, and impossible for the cat to be the opposite of what it is.

If you look at the world deterministically in which every reaction corresponds to a previous action, then it was always certain if the cat would survive the experiment, but the idea of possibility has nothing to do with what nature will do and everything to do with our own ability to predict it when we are uncertain.

Now let's apply this to your example.

Right now, World War III could possibly start on Sept 1, 2039 simply because neither World War III nor Sept 1, 2039 have been observed yet. World War II starting on Sept 1, 1949 is impossible, because we already observed it and its start date, but this start date was possible up right up until Sept 1, 1939 when it was observed turning uncertainty into certainty

To answer the first part of your question, you are correct: it is impossible for a thing to be possible once an observation to the contrary is made.

So why does World War II starting on Sept 1, 1949 feel more possible than people flying?

The human mind is designed for empathy meaning that we are able to conceive things not just from our own perspective, but we can imagine things from the perspective of others. We can open up Schrodinger's box, see the cat alive, and still imagine how a person who does not have our experience of opening the box might believe in the possibility of the cat being dead. This kind of empathy is a vital skill that improves our chances of survival by being able to guess what others think and how they will react if they don't know what we know.

So, seeing World War II starting on Sept 1, 1949 as a possibility, even though this contradicts our own observations feels natural because we can empathise with people from a time before the observation of the war started and understand the uncertainty in thier future. But Humans can not fly, we never could fly, and baring a significant advancement in our technology or biology, they likely never will. So this is not a thing we are drawn to empathise with; so, it feels like something that is more truly impossible.

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