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By actual possibility I mean the possibility which is implied by ability or power.

By logical possibility I mean whether concepts of reality contradict each other or not.

I believe that knowledge and reason are accurate reflections of the nature of reality. Therefore I am not inclined to believe that something which is actually possible in reality (like a free choice) could also be logically impossible (for example, an allegedly true prediction about the outcome of the choice). If the possibilities indicated by reasoning do not match the actual possibilities of reality, then it seems to me there must be a false premise which would explain the discrepancy.

Can anyone prove this either way? Can the actually possible also be logically impossible?

Can something be within the limits of ability/power/opportunity yet also create a contradiction if it occurred?

It seems that merely asking this question presupposes that logic and knowledge do indeed reflect the nature of reality in an accurate manner.

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  • You say that free will if possible, care to provide us with some evidence? Because, it seems quite impossible, and quite contradictory to our current understanding of physics.
    – jcora
    Jun 11, 2012 at 10:38
  • @Bane it sounds like you must utilize an inconsistent epistemology. You trust your conscious experience when it comes to external things like the laws of physics, but not when it comes to internal things like moral agency and self-determination.
    – Benjamin
    Jun 12, 2012 at 4:33
  • I agree with you and believe the universe is reasonable as you describe, but it cannot be proven in logic. There are many philosophers who believe there are true contradictions. They cannot make a winning case but they have their opinions. The dialethists for instance, and the materialists. A remarkable number of people believe in metaphysical ideas that cause contradictions (it seems to be an epidemic), but for the most part do not realise it so they don't count as knowingly endorsing contradictions. By Aristotle's definition nobody has yet shown that true contradictions can occur. .
    – user20253
    Nov 3, 2017 at 12:58
  • Check the EM Drive. Even NASA has validated that such propulsion system is actually possible, despite there's no explanation for it, ergo it is logically impossible.
    – RodolfoAP
    Nov 9, 2017 at 0:30

7 Answers 7

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If we use your own definitions,

By actual possibility I mean the possibility which is implied by ability or power.
By logical possibility I mean whether concepts of reality contradict each other or not.

then I would say that yes, it is straightforward to have something which is logically impossible but actually possible. The reason for this is that you do not specify which concepts — or models — of reality you are concerned with.

For a half-serious example, consider the dramatic revelation in Star Wars: Episode V (The Empire Strikes Back). Luke's reaction to the revelation that Darth Vader is his father is disbelief: that it is impossible. Whatever emotions drove this reaction, it is likely that this was his reaction to the fact that the assertion contradicted his mental model of Darth Vader and Anakin Skywalker being seperate individuals, one of whom literally killed the other, as Ben Kenobi described in Episode IV. Relative to this model of reality, it was logically impossible for Darth Vader to be Anakin Skywalker, because it violated an assumption used in constructing the model. But if we accept what is asserted or demonstrated by the later Star Wars films, it was in fact actually possible, and indeed true.

More seriously, discovering things which are actually possible but which are logically (more accurately, theoretically) impossible, is a good approximation to how science works according to Popper: by falsification. If a theory predicts that something should not happen (or is impossible to make happen), but which subsequently does happen, this invalidates the theory. For this reason, I would prefer to call this "theoretical", rather than "logical", impossibility, because it places the fault clearly where the failure of the model can more easily be remedied — by improving or replacing the theory.

In modern science, where we accept that probability may be an unavoidable feature of physical theories, we are presented with a more complicated situation. When a theory predicts one probability distribution, but experiment produces another, has the theory been falsified even if we assume that the experiment was "executed perfectly"? With probabilities, there is always of course a non-zero chance of freak occurrances in which events drawn from one distribution resemble another. This is of course less likely, the more random samples you take, but in most cases you cannot actually rule out the possibility that one distribution will in practise, with a finite number of samples, produce the curve of another. We then move from impossibility to improbability — where we might ask whether something is actually probable while being theoretically (or logically) improbable. This is a somewhat more nuanced, but still essentially Popperian notion of falsifiability: we accept that there can be such events, and that when they arise they indicate a failure of the theory.

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    A logical impossibility only makes sense if all its premises are true, if you find something which should be logically impossible, it must be because one of your premise are false. The "model" is simply just another premise you've assumed to be true.
    – Lie Ryan
    Jun 14, 2012 at 16:13
  • @LieRyan: I basically concur, which is why I recommend the notion of theoretically (as opp. "logically")(im)possibility as the pertinent notion corresponding the second definition of the OP. Of course, it is in principle possible that our notion of logical reasoning is itself not well-fitted to reality, but experience thus far suggests that it is parsimonious to amend the assumptions rather than the rules of inference.
    – Niel de Beaudrap
    Jun 14, 2012 at 22:09
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    You have not given an example of a contradiction - just a misunderstanding. I have down-voted this (sorry) because it seems very wrong indeed.
    – user20253
    Nov 3, 2017 at 13:01
  • @PeterJ: The question itself was a misunderstanding, in my opinion, and I was merely attempting to answer it on its own terms. It is not clear how something can be logically impossible without this being a consequence of rules of inference and axioms; and should it prove to be actually possible, this should meta-logically imply something about the relation of the rules of inference or axioms to reality. This seems true to me even exotic varieties of logic, though they more often embrace exotic possibilities (e.g. that of both a proposition and its negation) than exotic impossibilities.
    – Niel de Beaudrap
    Nov 3, 2017 at 18:30
  • @Niel de beaudrap - Fair enough. But you say 'It is straightforward to have something which is logically impossible but actually possible'. This is a very debatable assertion and I would say it is false. An argument for another time maybe.... .
    – user20253
    Nov 4, 2017 at 15:09
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The short answer is no: if something's logically impossible, then it isn't going to happen, not no way, not no how.

The distinction between logical possibility and other kinds is a little subtle though. It is possible to distinguish various kinds of possibility.

  • x is logically possible if and only if it the existence of x entails no contradictions.

The space of logical possibility is vast. There are dragons in logical space. There are worlds in which magic exists. There are worlds in which there are no physical laws. There are worlds in which nothing exists. The only things that there aren't in logical space are impossible things like round squares, or largest prime numbers.

  • x is physically possible if and only if the existence of x entails no violations of the laws of physics, as we currently understand them.

Everything that is physically possible is logically possible, but the converse isn't true. There is no magic in any physically possible world, because the existence of magic would violate the law of conservation of energy.

  • x is technologically possible if and only if the existence of x is compatible with currently existing technology.

Again, technological possibility is a subset of physical possibility. Faster than light transportation is not technologically possible (at the present) but perhaps it isn't physically possible.

The important point is that what is physically possible (what is compatible with the laws of nature) or what is humanly (compatible with human abilities) or technologically (compatible with current technology) possible is always a subset of logical possibility.

Take for instance, the question of God's omnipotence. God can do anything. "But God can't make round squares!" you say, "Therefore he can't really be omnipotent after all."

Well no. It isn't a limitation of God's power not to be able to make a round square because there is simply nothing that a round square could be. There isn't something such that God fails to be able to create it. A round square is just an absurdity created by our power to combine words that look meaningful even if there isn't anything they could possibly refer to.

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  • Good, but isn't physical possibility usually understood as a function of the completed laws of physics, rather than the current laws?
    – ChristopherE
    Feb 25, 2014 at 3:00
  • Technically yes. But there's a kind of famous problem about "completed physics" called Hempel's Dilemma. If the physical is what is described by "completed physics" then we don't know what the physical is, because we don't have a completed physics. But, if "the physical" means the world as described by current physics, then we know that the physical isn't real, because current physics is incomplete. I think the solution to the problem is a kind of approximation. We aren't all the way there yet, but current physics provides a very good approximation of reality, with some weirdness at the edges.
    – user5172
    Feb 25, 2014 at 12:38
  • Yeah, good, but physicalism is usually understood as a metaphysical claim (in the harmless, ontological sense), and embracing the first horn shouldn't bother a metaphysician. I'd think the better route is to define physicalism in terms of completed physics, and then apply it, if that's ever useful/necessary, using current physics as an approximation.
    – ChristopherE
    Feb 26, 2014 at 0:46
  • The worry with that horn is that physicalists are supposed to be committed to the denial of certain stuff. Physicalism is supposed to say there are no disembodies souls, or God, or the like. If we define "the physical" in terms of a theory we don't have yet, who is to say that that theory won't have room in it for such entities? That's the problem. I agree that it isn't a fatal problem, of course. But it's an issue that needs dealing with, nonetheless.
    – user5172
    Feb 26, 2014 at 0:50
  • It seems an error to bring in physics. The question is about logical possibility. The idea would be that physics will never over-turn logic, not that logic will never over-turn physics. So far nothing in physics suggests that there are true contradictions if we use Aristotle's definition. Metaphysics comes before physics as well as after and no physical fact can fail to conform to metaphysical logic. (Or that is the proposal here). . . .
    – user20253
    Nov 3, 2017 at 13:08
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Logic & Reality

  • We are (including logical structure) are the proper subset of the set (reality), therefore there will be no contradiction between the set and the proper subset

  • Logic derived from empirical observation, therefore logic won't be contradict with reality

Logic is merely a representative of such reality. There will be no logical structure if there is no reality.

If there is logically impossible according to a specific reality, then it doesn't mean that logic contradict to reality, but rather than that logic is not a part of a reality.

But once we know deeper and deeper about a new reality, and we know the structure, it automatically creates logical structures on our thinking, and there will be no contradiction one to another anymore.

If there is something can be actually possible yet logically impossible, it's merely because incompleteness on our logical thinking, mismatch on our thinking or it involves new structures of logical thinking. But as long as past logical thinking is correct logical structure, then it won't be contradicted to a new logical structure we found.

For examples:

  • Someone is flying to the moon in front of us, without a ship and a body protector ...
  • Our logical said that it's impossible ...
  • But then, we know that somehow through meditation, or such a process (called "pray") human body can produce such invisible protector and enable to distinguish a gravity.
  • Now, we found the logical behind this: meditation/pray -> produce such facilities (capabilities) to fly to the moon

Different reality may be has its own logical explanation. Our logical structures could absorb new structure of logical that related to a new reality. But it doesn't have to destroy the correct past logical structures. A correction for logical structures is permitted, therefore there won't be a contradiction in between logical structures and reality.

Besides, our logical is just our thinking. Logic follows reality (derived from reality).

Something can't be actually possible yet logically impossible.

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    I agree with your conclusion but I do not understand your reasoning.
    – Benjamin
    Jun 10, 2012 at 22:31
  • Hi, i already edited to add an additional assertions
    – Seremonia
    Jun 11, 2012 at 8:54
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Would it help if we rephrased the question to state: could man create something that is logically Impossible such as a circle-square or a four-sided triangle? I'm inclined to say, no.

For it to exist is to deny its logical impossibility.

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It is possible to have somthing that is actually possible but not logically possible. That is because logic requires apriori knowledge in the form of atleast one logical set of premise. Actuality does not require apriori knowledge. Therefore, a thing can be actually true in that it exist but logically impossible in that it is not derivable and logic is derivable.

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This is a good question, I've thought about it for a while and I think I have a counter example. In 2010 there was a research paper published in the Journal of Personality and Social Psychology by Daryl J. Bem called Feeling the Future, a series of experiments supposedly demonstrating the existence of 'retroactive priming' .. In psychology one fairly well known effect is that of subliminal priming, typical experiments include brief presentation of a word at a speed below that which is required to cross the threshold of awareness, the presentation of a stimulus that will be either congruent (eg. prime - word 'happy' stimulus - puppies) or incongruent (eg, prime - happy and stimulus - rotting meat) with the prime. Participants are then asked to press a button indicating whether the stimulus is happy or sad. Participants are faster to respond correctly when the stimulus is preceded by a congruent prime. This is a widely demonstrated and repeated effect.

The genius of Bem's work was to change the order of this sequence. Instead of the normal prime-stimulus-answer, Bem tried Stimulus-answer-prime - and got a significant effect.

Retroactive priming, if it exists, is proof that future events are able to affect present events. This i think would constitute an example of something which according to logic should not happen .. and yet, seemingly, it does. So yes, i do think that the logical impossibility of an events occurrence is not necessarily conclusive proof that it cannot happen in the world

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  • why was this downvoted ?
    – Dr Sister
    Nov 18, 2014 at 6:48
  • The argument for events preceding their causes, perhaps?
    – user16869
    Feb 9, 2016 at 2:02
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Can something be within the limits of ability/power/opportunity yet also create a contradiction if it occurred?

Yes, this happens all the time-- so often, in fact, that we usually fail to even notice it.

Let's take, for a preliminary example, Russell's barber paradox. We imagine a town, in which all of the men who are not shaved by the barber shave themselves. This means, of course, that the adult male residents of the town can be cleanly divided into two groups, those that are shaved by the barber, and those that shave themselves. And, of course, it means that each man can be placed into one group or the other. In which group do we place the barber?

More to the point, think of Zeno's paradoxes which irrefutably prove, using impeccable and unassailable classical logic, that motion is impossible. And yet in reality, things move.

As a final example, let us take a simple mathematical example (since arithmetic is generally considered to be well-founded in logic): one gallon of gasoline plus one gallon of water does not yield two gallons of anything.

It's worth noting that the question here makes no reference to the type of logic to use; I've presumed classical logic for these examples, but similar examples could be found for any of the many forms of non-classical or deviant logic that have been proposed.

In short: there are limits to how well any logic can represent the actual world. Furthermore, no logic can be proposed that does not rely on unprovable axioms, circular reasoning, or infinite regress. So it goes.

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    The barber thing is a false dilemma. Zeno's paradoxes mistake the inability of an analyst to complete a recursive measuring function for the actual inability to occur. I've never heard of the water and gas thing you mentioned. I would hate to be the one betting there is no explanation for it. It is interesting that you mentioned types of logic. I am just referring to the rejection of contradictions. The form of reasoning in which contradiction implies a false premise.
    – Benjamin
    Jun 12, 2012 at 19:14
  • The barber thing is not a false dilemma; it is an example of a situation where logic breaks down. There are literally hundreds of named paradoxes which demonstrate similar things. As for Zeno, you are misreading the situation-- Zeno has four different arguments that cover four different possibilities: that time is continuous and space is discontinuous, that space is continuous and time is discontinuous, that space and time are both continuous, and that space and time are both continuous. None of these possibilities allow motion to occur.
    – Michael Dorfman
    Jun 12, 2012 at 19:26
  • As for types of logic, you should then stay away from Dialetheisms such as Paraconsistent Logic, as they permit "true contradictions".
    – Michael Dorfman
    Jun 12, 2012 at 19:27
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    The barber shaves himself which puts him into a third category. The "paradox" wrongly assumes two categories. It is a false dilemma to ignore the glaring overlap of those shaved by themselves and those shaved by the barber. Re Zeno: recursively dividing by half doesn't change anything about reality it just keeps you real busy while reality moves on without you.
    – Benjamin
    Jun 12, 2012 at 20:30
  • The "third category" (or tertium datur) is precisely what is at stake in the Law of the Excluded Middle, in the canons of Classical Logic. As for Zeno, I suggest you that if you look at his arguments in some detail, you'd see how profound they are. For example: the Dichotomy argument refutes the notion that space can be continuous while time is discontinuous; if there is a minimal discrete quanta of time, and no minimal discrete quanta of distance, one would require an infinite number of time-quanta to go a finite distance. When you couple this with the other 3 arguments, you're stuck.
    – Michael Dorfman
    Jun 12, 2012 at 20:38

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