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[Source:] Counterfactuals have this form: If [S:] P were true, Q would be true.

Material conditional: If [P:] P is the case, then Q is the case.

Counterfactuals are not material conditionals! [Does the following para proves this by contradiction?]

[I split the longer sentences here:] [For want of a contradiction, assume that counterfactuals ARE material conditionals.] A material conditional will be true whenever the antecedent is false. But this can't be the case for counterfactual conditionals since their antecedents are always false, and so every counterfactual conditional would be true. But every counterfactual conditional is not true. Thus counterfactuals are not material conditionals.

Call the first bolded protasis S (for present Subjunctive tense) and the second P (for simple Present tense). Besides the difference in grammatical mood, how do they differ?

  • If the English subjunctive were a 'tense' then that 'tense' would be imperfect past future: 'would' is the imperfect past form of the future tense marker 'will'. It can often make sense to consider a statement in the present subjunctive to express the future that would proceed from a different past. If that is not helpful, then realize that formally it is not a tense but marks 'mood' in English, in the sense of 'modal logic' which is concerned with alternative possible worlds. – jobermark Nov 3 '14 at 15:28
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The language in the first statement is meant to invoke a hypothetical scenario, whereas in the second I am merely making a statement about the world as it currently is.

The difference has to do with the truth value of the statement itself.

A Material Conditional statement is true as long as for every situation in which the first part is true, the second part is also true. It makes no guarantees about the logical coherence of the statement when applied to hypothetical situations. Technically any statement of P->Q is true as long as either P is false or both P and Q are true, regardless of whether or not there is any causal connection between P and Q.

A Counterfactual is making a statement about necessity that states that regardless of the current truth value of P, if things were ever in a condition in which P were the case, Q would also be the case.

Here is an example I stole from wikipedia to illustrate the difference:

Counterfactual: If I were in Poland, I would be in Europe. (true, though the method to evaluate such truth is hotly contested)

Material Conditional: If I were in Poland, I would be in Africa (also true, because I am not in Poland so this has no binding effect on the truth or falsehood of the second part)

What we usually want when we discuss things in real life is the counter-factual. It is not making a claim about the real world only, but also about hypothetical ones. This is how we usually think and what we mean in colloquial speech when we say "If... then..." most of the time.

  • Thank you. Sorry for my naivety, but I don't understand your answer, because the diction seems too abstract and complex. May I ask if you would please please explain as though I were 10 years old? For example, in the 1st sentence of your para 4, what's necessity? – Greek - Area 51 Proposal May 3 '15 at 22:32
  • With a counterfactual you are reasoning about things that aren't true as though they were. So when you're thinking about a unicorn, you can say stuff like, If I were to see a unicorn, it would have only one horn. But with a material conditional, the only thing that matters is "If the first part is true, the second part has to be true." If the first part is false, it doesn't matter what the second part says at all. It doesn't have to make sense. So "If I were to see a unicorn, green cheese would start falling from the sky" is a perfectly legitimate material conditional, since part 1 is false. – Jason Bray May 4 '15 at 5:37
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As a man, who is six feet tall, I can say "Were I a woman, I would be less than six feet tall" and have it mean something. It is a prediction of how the world might be different if we changed one thing. This is what logicians mean when they discuss an alternate world.

I can say "If I am a woman, I am less than six feet tall", and it is nominally true, because the condition is false, but not in a way that means anything. I could equally say "If I am a woman, the moon is made of green cheese." and it would be equally meaningful.

However, saying "Were I a woman, the moon would be made of green cheese" indicates the two things are related for some reason and that my gender would be likely to actually affect the substance of the moon, which is nonsense.

So changing the mood here changes the statement from true but pointless, to theoretical and highly unlikely.

[This is hard to keep track of because the English subjunctive looks too much like the past tense, and people just fail to use it most of the time, or they use the past tense instead. Folks often say "If I was there", when they mean "If I were there".]

Also, there are variants of "would" that slightly alter the kind of alternate world the sentence is indicating. For instance, if I said 'might' instead of 'would', it indicates that the difference would not be logically implied by the change in the world, but would make it possible. "If I were a woman, I might wear pink more." means that my being a woman would make that possible. It would not necessarily happen, but it surely is not going to happen as long as I am a man. If I said 'should' it would imply things would be disapproved of in the alternate world because of social convention or moral sense, rather than actually being different. "If I were a woman, I should wear a shirt." But as I am a man, and it is 80F, I have mine off and no one cares.

[Again, hard to learn, because these are rules many people just fail to follow. The precise intentions behind words like might, may, should, etc. drift around a lot because they are poorly used. It is so bad that when it is necessary to insist they be used correctly, for instance in military specifications, people insist that their definitions be stated, even though they are being used with their traditional meanings.]

Logic models this as if all of the possible worlds created by changes to this one already exist, and we are just picking which ones to imagine working in. This is in principle silly, but it gives a clear way of discussing alternatives.

You can imagine that every counterfactual conditional is true in some alternate world. In impossible worlds, everything is true and false at the same time, and in possible worlds, the counterfactuals that are really true have true conclusions.

The problem is that the subjunctive places the statement in the realm of alternate realities and not actual reality, and without specifying which possible world you are talking about, the statement becomes true but useless. We need to know what kinds of rules we imagine are not changing when we change the thing we have chosen to change. Only the worlds that change what we intended and do not change the rest are allowed in an interpretation.

In situations where the range of allowed possible worlds is well-defined, either explicitly or by context, the subjunctive form becomes declarative when combined with that definition included in the premises. So suppose we said "Because of basic biology, if my other genes did not change, if I were a woman, I would be less than six feet tall." Then I can tell what is to be kept fixed when I consider the alternate gender, and only padded out in this way does the sentence have real and definite logical content.

Generally, we can guess what the omitted premises are, and we just don't say them. But if we cannot guess them, we just have to act as if the false conditions are meant to be taken literally, and the statement is just true but meaningless.

With this interpretation, the same is true of statements of obligation, those 'should' constructions, and of statements of mere potential, those 'might' constructions. They are all true all the time, but only meaningful with additional premises.

  • Thank you. Sorry for my naivety, but I don't understand your answer, because the diction seems too abstract and complex. May I ask if you would please please explain as though I were 10 years old? For example, what's some alternate world? What do you mean by unstable? What's a range of allowed possible worlds? – Greek - Area 51 Proposal May 3 '15 at 22:31
  • So now that is unfortunately long, but it explains the grammar as well as the logic. – jobermark May 4 '15 at 0:00
  • Thank you again. Sorry to bother you again, but just 2 remarks: 1. Is the last word of your para 2 right? Did you mean 'meaningLESS'? 2. Also, would you please check this sentence: If I said 'should' it would imply things would disapproved of in the alternate world because of social convention or moral sense ? – Greek - Area 51 Proposal May 4 '15 at 1:43
  • I did mean 'meaningless'. Counterfactuals where you cannot guess the context are just as meaningless as indicative statements with false premises like "If 2+2 = 5 then all dogs are purple." but many strict logicians would say both are still true. – jobermark May 4 '15 at 2:14
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Logically, both forms are identically. The only difference is the expectation of the reader. If you start with "if P were true", then the reader expects an ending like "then Q would be true, but since we know Q is false, P cannot be true".

That ending might not come. A famous example is geometry, where it was assumed for a long time that the "parallel postulate" of Euclidean geometry could be proved. Many mathematicians tried to find a proof by contradiction, and ended with "then Q would be true, and Q is really really weird, but we cannot show it to be wrong".

In the end, "were" had to be replaced with "is" and we got hyperbolic and elliptic geometry.

  • "If I were to get up an hour earlier, I would get here on time." is not logically equivalent to "If I get up an hour earlier, I get here on time." The former is a supposition, suspended in some alternate situation which is not really specified. The latter is a fact about a real observed trend. The conditions are clear -- you are simply assuming events are repeatable. – jobermark Nov 3 '14 at 2:00
  • Both the comment and the answer are correct but the operant point is what is meant by "logically" I take it that gnasher729 means by this "in sentential logic" whereas jobermark is invoking a more complex logic... – virmaior Dec 3 '14 at 5:29
  • Sorry, but it’s unclear to me how this answers my question. For example, you wrote both forms are identically. Was this what you intended to write? – Greek - Area 51 Proposal May 3 '15 at 20:34

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