Consider the following hypothetical question:

If there were two moons, what kind of poem would be composed?

There are two ways of considering this type of statement that I find unexciting:

  1. Any answer for this question is true, since the premise is false (as an application of the principle of explosion)
  2. We can't say anything, since the change may result in large differences in later state and prediction is impossible.(butterfly effect)

I think that both solutions are inadequate and there ought to be a theory that deal with this kind of contradiction.

Can anyone help me to better understand how to understand these sorts of conditional questions.


In ordinary conversation, counterfactual propositions are not trivialized, and I seek such theories that counterfactual need not trivialized and ordinary reasoning are constructed in that theory.

For example, I think the question "What would you do if you were born rich?". I think the answer from a strictly scientific point of view of would be as follows:

"If I was born rich, almost everything about me would be different from this world, and to begin with, it is not even clear whether an I with the same personality would exist, so I can't say anything."

It's not false, but people don't answer in such a way. They might answer as "I would eat expensive food every day, live in a mansion, and ..."

These sorts of answers seem to have their own truth values. If the person answering is someone who likes tennis, they may says "I would buy my own tennis court.", this seems to be true, but if they don't like tennis and instead are a fan of something else, it must be false.

  • If you're going to kick out explosion and kick out the idea that we couldn't predict, then you're going to have to make clearer what the rules of the thought experiment are before this question can be answerable without just wandering into mere opinion. – virmaior Jun 10 '15 at 10:58
  • @virmaior I don't think the question is opinion based. The two moon / poem is just an example, but this is a generic question on counterfactual reasonning (or this is how I interpret it, the author can tell us if s/he agrees) – Quentin Ruyant Jun 10 '15 at 11:01
  • @virmaior actually your comment is a good answer to the question: we need rules to evaluate counterfactuals. – Quentin Ruyant Jun 10 '15 at 11:04
  • The principle of explosion is not applicable because this is a counterfactual proposition that cannot be evaluated in propositional logic (propositional logic concerns only what is actually the case). Counterfactuals talk about possibilities. We need context to evaluate what kind of possibilities are at stake. – Quentin Ruyant Jun 10 '15 at 11:09
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    I don't think you've quite grasped the idea of contradiction or explosion here. These premises aren't contradictions - they're just contingently false. The solution isn't to form an alternative logic with true contradictions but rather to propose a theory of counterfactuals or alternative possibilities, and plenty such theories exist e.g. en.wikipedia.org/wiki/Modal_logic – Paul Ross Jun 10 '15 at 12:33

As noted in comments and other answers, the principle of explosion is not applicable in this case so the first answer is invalid.

You probably had in mind the fact than in logic, "if A then B" is trivially true when A is false. But that doesn't apply to counterfactuals. Your sentence is not "if there are two moons, ..." but "if there were two moons, ...". That makes all the difference! Simple propositional logic is not the proper tool to analyse conditionals. It is a tool to talk about what is actually the case, not what would possibly be the case.

Thus your (1) is an incorrect answer but your (2) can still be considered.

As noted by virmaior, counterfactuals can be analysed in terms of possible worlds (and modal logic is the right tool for that).

However before talking about possibilities and impossibilities we must specify what possibilities are at stake: are they technical possibilities? Physical possibilities? Logical possibilities?

Take the following statement:

"I am now in New York, but I could be in Paris within a few minutes."

Well no, this is technically impossible. However it is physically possible since I wouldn't exceed the speed of light. Only the technology is missing. I could add to the sentence "if I had the technology to travel that fast" and the sentence becomes true. Or just imagine the sentence pronounced by a Star Trek character, and it becomes true. And if you stick only to logical possibilities you can even break the laws of physics if you wish!

What this example intents to show is that counterfactual talk is very sensitive to the context and that the truth value of a counterfactual depends on additional assumptions.

What the context fixes is a set of rules regarding what can change or not from possible worlds to possible worlds, i.e. what is necessary or not.

Generally, locutors assume something like a ceteris paribus clause (all things equal), which means that you should change the minimum possible to render the counterfactual true: all the rest should remain fixed. A ceteris paribus clause could help understand how one would typically respond to your example questions: if there were two moons, but all the rest remains unchanged: poets are inspired alike by moons, etc. If I were rich, but my personality, desires, tastes remained the same.

That explains why your (2) is inappropriate. (2) assumes that the only relevant rules regarding what remains unchanged in other possible worlds are the laws of physics. It's not how people generally understand counterfactuals: thay assume a maximum set of things remain true in these other possible worlds. This is also why counterfactuals depend on the context (while physical laws are not contextual).

If you want authors who reflected on counterfactuals, you can have a look at David Lewis for example, or Maudlin's "metaphysics within physics" (more about laws of nature, but there are parts about counterfactuals).

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  • @user53216 Goodman "Fact, Fiction, and Forecast" is also a good read on the subject a lot of contemporary discussions stems from his observations, so it's a good introduction! – Quentin Ruyant Jun 12 '15 at 15:37

I think there's a lot going on in this question, which is part of why I initially closed it prior to revision -- which made the purpose substantially clearer.

First, Paul Ross hits the nail on the head in the comments in terms of the techniques we use to evaluate these sorts of statements, which are called counterfactuals. Modal logic is the set of logical methods devoted to looking at necessity and contingency.

I do agree that "principle of explosion" is misapplied here, but I can see why you went for that term. A better term would be "vacuously true" which refers to those claims that are true but bear no relation to the world as it is. But with modal logic, we can evaluate counterfactuals more substantively than stopping at vacuous truth.

Often this ability is referred to as "visibility" of one possible world from another. In other words, in this world, we see that you are a tennis lover, so we can see in a visible world where you are a tennis lover and rich, that you would there buy a tennis court.

Second, there's a similar question in the literature or perhaps two. The first that comes to mind is the Twin-World Thought Experiment put forth by Hilary Putnam. Ostensibly, the question is whether it really matters that water is H2O, but the relevance I see to your question is in one type of response to this (which happens to be the one I subscribe to) says that the claim that twin-world XYZ-"water" can function exactly like water to us is a claim that collapses under scrutiny, requiring us either to make XYZ water or to be telling a type of fantasy where we should just stay away from the layer of chemical composition in our possible world.

In other words, relating back to our modal logic, I think it's fair sometimes to deny that a different world really could be like our world in every way but a minor tweak (like me being employed at Harvard instead of at a minor university in Japan). For instance, it seems deniable to me to "imagine you are exactly like you are now but a giant lizard that eats flies" -- since I cannot be "exactly like I am now" but simultaneously a lizard instead of a person.

But this isn't quite "butterfly effect" in my view. Instead, it is that any thought experiment needs to make clear what has changed and needs to be a plausible set of changes to result in meaningful counterfactuals.

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I would point you at my previous answer about the function of 'might' from a Wittgensteinian perspective, rather than that of Kripke worlds or formal modal logics https://philosophy.stackexchange.com/a/16454/9166.

I feel that the 'mutable modality' often reflected by 'would' and 'might' should not be construed as an absolute construct with a propositional meaning. I also think it is a bad choice to reify "all possible worlds". Possible is not meaningful enough, and All is likely to net you a lot of paradoxes. So it is better to look at this kind of thing, that looks like a condition, as a request, instead.

Even when the contents are factual, and not counterfactual, this kind of statement does not convey meaning. It conveys trust or mistrust of how well the fact has been incorporated into a theory. In the counterfactual form it considers whether and how the changed fact might incorporate into a theory.

The theories that might result lie in a range that depends on how tightly other parameters in the definition of the world are bound to reality, and how tightly our theory of the world already binds together the parameters that are allowed or forced to vary by the change. Unlike in the purely factual case of using models for validity testing, these models are not created equal. Some are better than others.

One way of looking at the naturally occurring preference between potential implications comes from a scientific perspective. Good answers are 'parsimonious'. In this case, what I mean by that is that a perfect answer would involve the least change to other unmentioned parameters and therefore would have the shortest additional description, if you tried to write down a minimal list of premises that should imply all of the differences between that world and reality.

The most parsimonious solution is not the solution that reflects minimal change of facts, because for there to be two moons and for that to have not affected poetry would require an explanation of its own. It would be unnatural to human psychology. (For instance, the two moons should evolve some kind of contrasting meaning. Or, if that did not happen Sun vs Moon should somehow become a triad in mythology, which would affect the whole history of the Apollonian/Dionysian or 'Warrior/Lover' duality.) One would need to inject premises to explain the lack of the expected effect, and in the end these would involve more extra structure than letting the logical implications play out and only adding reconciling premises.

Of course this 'parsimony' is largely subjective, or at the very least statistical and vague. To try to write down a full list of variations between two scenarios in detail would be a silly task, and no one will ever undertake it. And to trying to make any reasonable set of premises minimal has a pronounced history of failure. (At the very least, presuming it is generally possible solves the halting problem.)

But I think, in a very broad sense, this is what we really want as an answer to this kind of question: A most parsimonious adaptation to the new parameter in the appropriate solution space.

In science, it is a parsimonious edit of a theory that covers a potential outcome. In a software design, it is a shift in defined terms that provides a potentially desired power with a minimal quantity of rewriting. In this form, it is the most compelling 'science-fiction backstory' that adapts to the new premise.

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