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Is it consistent to say something like "Possibly there is a cat in my room, but in fact there is not"? Basically, is it consistent to assert that something is possible but in fact not the case?

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    Consistent with what? Of course there are frameworks in which it's consistent. – Noah Schweber Jan 5 at 3:21
  • I have a car that's capable of driving over the speed limit, but I can choose not to. – Barmar Jan 5 at 15:53
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    In modal logic, if P is the proposition "There is a cat in my room", the formula "♢P ∧ ¬P" is true precisely when P is possible and false. – chepner Jan 5 at 19:11
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    Someone asks you, "Do you have a cat in your room?" You know there is a cat in your room. You look over and see the cat. As you watch the cat walk to the door, you say "Possibly there is a cat in my room". And then, as the cat walks out the door, you say "but in fact there is not". – Kevin Fegan Jan 6 at 3:55
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    Note there's a difference between natural language 'and' and 'but' that does not carry over precisely into formal logic. answers.yahoo.com/question/index?qid=20110121160804AAU8VnV – J D Jan 6 at 8:21
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Well, in English you would use the subjunctive tense and say, "possibly I could have had a cat in my room, but in fact I do not." That's a reasonable statement to make. "I could have been a doctor" is another statement of the same kind that is considered normal to utter. The meaning of such statements is tied to an implicit idea of some difference in the world that would have caused the proposed situation. "I could have had a cat if it wasn't for my landlord," for example.

This is essentially a counterfactual claim. We imagine some scenario, alternative to actual reality, and ask what would result, counterfactually, from that scenario.

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  • That's a good, clear answer, and I love the reference to the "subjunctive," the most grammatically abused tense. But are you suggesting that these "possibilities" are artifacts of language in the logical positivist sense? Or do you have some idea of the nature or "ontology" of "possible" events or things? Honestly, I have no idea, so just wondering. – Nelson Alexander Jan 5 at 4:31
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    Consider this example: "If you arrange five black stones and seven white stones in a row, at least two white stones will be adjacent to each other." If you haven't actually arranged the stones, this is a counterfactual statement. Those stones don't exist. And yet it is absolutely true, and not simply a result of the way we use words; it's a property of stones-arranged-in-rows, not of words. – causative Jan 5 at 5:07
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    As long as the stones are arranged in a row, the statement is true of them no matter what order you arrange them, which can be shown mathematically because of the pigeonhole principle. If you move the stones out of a row shape, the statement simply isn't applicable to those stones. But it remains a true counterfactual statement even when there are no real stones that it applies to. – causative Jan 5 at 6:30
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    Similar example: "This proof would work if 2 were not prime." In fact 2 is prime, and will always be prime at every moment in any universe. And yet it's a reasonable counterfactual statement for a mathematician to make; it probably means something like "the only flaw in this proof is the mistaken assumption that all primes are odd." – Charles Staats Jan 5 at 15:47
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    @NelsonAlexander The dichotomies are idealism and realism, and rationalism and empiricism. The first speaks to the tenability of external reality and is ontological, and the latter speaks to epistemology because it claims knowledge comes from reason or the senses, respectively. I like your attack on the existence of events by denying infintesimals of time. Very process philosophy of you! – J D Jan 6 at 8:17
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Yes, certainly. I would like very much to hear from others, because the ontological status of "possibilities" interests me greatly. But I'm afraid that a real answer to your question might involve almost all of philosophy.

Meanwhile, one simplified description of Shannon information theory, is that it involves the reduction of a set of "possibilities" by a process of elimination to an "actuality," in this case "all possible sounds" reduced to the intended word by division and selection, as in a game of 20 questions.

On a more grandiose scale Hegel's abstruse statement that the "rational is the real" and vice versa could be restated as "the possible is reduced to the actual." Loosely, the "possible" being what we can conceive of and the "actual" being that which we can "act upon," the physical or material "reality."

The "possible" always exceeds the "actual." So the actual or factual is an elimination of the possibilities, as Sherlock Holmes put it. So it is perfectly consistent to say there is a "possibility" inconsistent with, yet coexisting with a "factuality."

Yet, "coexisting" raises the problem of time. Is every "possibility" even logical contradiction, resolved and superseded "over time." Two statements may not be true "at the same time." So in the end is time itself the transformation of all possibilities into actualities?

Well, here is where we arrive at what is formally known in philosophy as a "stoner question." So, I leave it there and really hope some better answers are forthcoming.

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    Famously, David Lewis was a modal realist and defended the idea that possible worlds are just as real as the actual world, and hence possibilities, including counterfactual possibilities, have full ontological status. For Lewis, the only thing that distinguishes the actual world from other PWs is that it happens to be the one we find ourselves in. I think Stalnaker also believes that "ways the world could have been" are real, though his realism is not as thoroughgoing as Lewis. – Bumble Jan 5 at 11:30
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    If you interested in modality consider giving plato.stanford.edu/entries/modality-epistemology a read. – J D Jan 6 at 8:25
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In proper English, you would have to say for example:

X is possibly true and X is false.

In practice, you would say instead, for example:

Yes, X is possibly true, but in fact, it is false.

But the meaning is the same.

Compare:

X is either true or false.

X is both possibly true and possibly false.

By definition, a logical variable is a priori both possibly true and possibly false.

And it is, also by definition, either true or false.

This distinction is crucial to formal logic.

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Something can be false as of now but might become true in the future. Therefore, X is possible but false makes sense and is consistent.

For example, time travel is possible(according to few people) but false as of now.

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  • This is just a matter of the inexact natural language. In "X is possible" X describes a state now or in the future. In "X is false" X describes a state now. (We cannot generally make truth statements about the future.) For example "It is possible that it rains but it doesn't" means "possible today but not raining right now". Because if you take "it is possible that it rains" as a statement about the present, and it does not presently rain, then it does not rain bacause it is impossible (or it would!) -- for example the temperature is too high or the moisture too low. – Peter - Reinstate Monica Jan 6 at 11:59
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Yes it is consistent. Let's take a claim: X is possible The reason why we can say that X is possible is one of the 3 following:

  1. If we know X is true. By definition, if it is true, then it is possible.
  2. There is no way to know if X is true or false. As an exemple, X could be an event in the future, so there are no certain way to know if X is true or false.
  3. X is false (or true but that also fits the first category) for a fact but that is unknown to some.

It is with the 3rd category that makes your sentence consistent. The word "Possibly" is relative to an observer. When you say Possibly there is a cat in my room, it is a possibility for any observer who doesn't know for a fact that the cat is not there. However it is not a possibility for you, if you know for a fact that the cat is not there.

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Another common meaning is to say that X is superficially possible, but false. In cases where one has been trying to analytically demonstrate whether X is true or false, and the analysis has not proceeded far enough to disprove X, the implication with or without the word "superficially", would typically be that there might be visible evidence that, if analyzed, might show X false, but one doesn't know whether any of the evidence that is visible meets that criterion.

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Is it consistent to say something like "Possibly there is a cat in my room, but in fact there is not"? Basically, is it consistent to assert that something is possible but in fact not the case?

As has been implied in comments and elsewhere, the English Language is not an adequate vehicle for formal logic.

You have failed right at the start to say what you mean by consistent. The statements are grammatically consistent but in terms of meaning they may or may not be according to what you think the sentences mean.

In order to give a formal answer, the question must be stated within a formal system where all the terms (false, possible, consistent, assert, etc) are clearly defined. Of particular importance is the meaning of "possible". Are you referring to a level of probability? If so, you could say that an event is possible with a zero level of probability.

If this seems too theoretical, bear in mind that humans are often blinded by common sense. No-one has successfully explained some of the results of quantum physics in common-sense terms because, in terms of human experience, they simply don't make sense at all.


[Quantum mechanics] describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd. Richard P. Feynman

There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time ... On the other hand, I think I can safely say that nobody understands quantum mechanics. Richard P. Feynman

Richard Phillips Feynman ForMemRS (/ˈfaɪnmən/; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, as well as his work in particle physics for which he proposed the parton model. For contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. https://en.wikipedia.org/wiki/Richard_Feynman

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Whether “[statement] X is possible but false” is a contradiction depends on the definitions of "statement", "false" and "possible" ;-).

  • What is a statement? For simplicity we assume an objective reality which can be readily perceived (which implies, for example, that we do not sit in Plato's cave or are simply imagining things). To state X means that "X" is an objective fact in the common sense of the word.

  • Let's also assume that "false" has its common meaning consistent with our assumption of an objective, readily perceivable reality: It is then almost redundant ("X is true" means "X", and "X is false" means "not X").

  • What is "possible"? We'll explore two common meanings and see how they affect your sentence.

    1. "X is possible" means "there are no obstacles preventing X". For example, it is impossible that this glass of water lies on its side on this table and is full of water. It is possible though that it stands upright, full of water.

      This leads to immediate problems with your sentence. "This glass stands on this table, full of water, is possible but false" is a contradiction: If it is false then it is presently impossible because the glass is in the kitchen, or for some other reason. Whatever part of reality deviates from this statement and prevents it from being true makes it presently also impossible. We could say, as in Nelson Alexander's answer, that all potentials have congealed to an objective, unambiguous reality, at least in this branch of the multiverse (if I may digress). The present in this simplified everyday epistemology leaves no room for uncertainty. It is what it is, and everything it is not has become impossible: The glass is broken, I have missed my plane, and dead is dead.

      We can use "is possible" with a statement about the future: "It is possible that it will rain tonight." "X" here is "it will rain". But this also leads to problems with your sentence because we generally cannot say about future events that they are false — unless they are utterly impossible, which would make your statement always contradictory.

    2. "X is possible" expresses not only an absence of obstacles but additionally a lack of information. For example, I don't know whether the glass stands on the table with water in it: Somebody else may have put it there. This also leads to problems: The same observer cannot express certainty and uncertainty about the same thing at the same time ("possible [shrug]" AND "known to be false").

    3. "X is possible" means, as in 1., that there are no obstacles; but it implicitly concerns not only the present but extends some time into the future. This is not uncommon in casual speech: "It is possible to die by a lightning strike." One problem with your sentence is then, as before, that we cannot generally say about events in the future that they are false. I would also argue that the time aspect of "X is possible [sometime in the future]" is part of the statement made. In other words, we still make a statement "Y is possible" (with "possible" meaning 1.), but the statement Y contains a core statement X and a time interval during which we think it is possible.

      Note that we probably also, generally, need to specify a location when we talk about possibilities. For example it is impossible to be killed by a lightning strike in a cave, and of course it will be impossible after the humans have died out or after the Earth has been absorbed when the Sun becomes a red giant. A completely specified statement X therefore would be surprisingly complex, along the line of "it is possible that some time in the future, on some places on the surface of of the Earth, as long as there are people, an Earth and an atmosphere, that a person gets killed by a lightning strike." The beauty of interpersonal communication is that all these side conditions are obvious and implicitly understood by the communicating parties and typically don't have to be made explicit. Needless to say that implicit assumptions may be wrong and may differ between sender and recipient. The last issue becomes apparent when talking to AIs.

      I would therefore, for clarity, reject this definition of "possible" and relegate all time and location and other constraints to the statement X.

So unless we modify our concept of reality and what it means to make statements about it — in other words descend into the "madness" (Paul Feyerabend) of epistemology and truth theory — your sentence is always contradictory.

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