# How do the antecedents of material and counterfactual conditionals differ?

I abbreviate 'Counterfactual Conditional Statements' to CCS and 'Material Conditional Statements' to MCS.

Source: p 338, A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley

Subjunctive conditionals are often called counterfactual conditionals because their antecedents are typically false.

1. Why does the quote above emphasise the falsity of CCS's Antecedents? MCS can also have false antecedents; so what? What differs? For example:

2. If E is a rare element, then E is costly.
3. If E were a rare element, then E would be costly.

Most physical objects are NOT rare elements; so both 2's and 3's antecedents are false.

• At a first approximation consider the difference, as this paper nicely summarizes, to be one of grammatical mood. You have material conditionals like "if A didn't happen, B did" and subjunctive conditionals like "if A hadn't happened, B would have." There is a genuinely subtle distinction: material conditionals can be thought of as solving truth-value tables - you find where the antecedent falls on the table and drag your finger across the whichever conclusion that permits you to make of the conclusion... May 3, 2015 at 23:59
• ...in subjunctives there is a fundamentally different structure: you take a time machine, go to the moment the variable in the antecedent is relevant, and tweak it to match your conditional. There is then a propagation forward by which you arrive at the conclusion. This is why subjunctives have historically been calculated with possible world semantics, and more recently are being understood as statements concerning causal models (personally I find the latter much more reasonable and think applying Kripke to counterfactual conditionals is silly, but that's just my plug). May 3, 2015 at 23:59
• @commando "more recently are being understood as statements concerning causal models" is genuinely interesting – I wasn't aware. Can you provide any source materials to follow up on? May 4, 2015 at 9:06
• "If E were a rare element" implies that E is not a rare element, while "if E is a rare element" does not imply such thing. May 4, 2015 at 22:08

Answering your question properly would require a whole book. I have a shelf full of books on conditionals, having studied it a fair bit and the very short answer is:

1. What elementary textbooks of logic tell you about conditionals is wrong. Real conditionals do not behave like material implication. Even if you try to rescue the account by restricting the assertability of conditionals using pragmatic maxims it still doesn't work.

2. The distinction between so-called indicatives and so-called counterfactuals is greatly overstated. They are not as different as most accounts make them out to be. Very commonly, exactly the same thought can be expressed indicatively and counterfactually, just by shifting the epistemic perspective.

3. The assertability of a conditional is (with a few odd exceptions) completely independent of whether the antecedent is true, false, unknown, undetermined, or even impossible. As such, the term "counterfactual" is misleading as a classification of conditionals unless it is used simply to mean a conditional with a false antecedent.

4. The subjunctive mood in English is actually quite rare. Just because a conditional contains "would" and "were" does not make it subjunctive. As such, trying to classify conditionals by their grammar is also misleading.

5. A lot of real conditionals are used to express relationships that are not certain - arguably there is little that is certain in real life. For a great many conditionals, 'if A then B'
is better understood as: 'it is highly probable that B, supposing A'.

6. Conditionals can only be understood by reference to the pragmatics of their usage: trying to give an account of their semantics on its own is futile. In fact, some commentators have gone further and claimed that conditionals don't have a semantics at all and are just pragmatic devices (though I don't agree with this).

7. The meaning of a conditional is not the same as the grounds one has for asserting it. Many conditionals are used to express a hypothetical inference from A to B. This inference could be causal, deductive, inductive, abductive, analogical, etc. These are different kinds of grounds, not different kinds of conditionals.

• Some kind of conclusion would be nice, some kind of reference all the better, but I like this answer. Nov 30, 2015 at 16:32
• Well to address the question directly, yes the questioner is right to say there is little difference between sentences 2 and 3. 2 would be appropriate if the speaker is unsure about E being rare, while 3 suggests the speaker thinks it is unlikely. But the difference is not great in the present tense. Both are asserting that being costly is inferrable from being rare. As to references, I like Rescher's book Conditionals, Bennett's A Philosophical Guide to Conditionals, Adams' Logic of Conditionals and Edgington's paper On Conditionals (in Mind (1995) vol.104: 235–329). Nov 30, 2015 at 17:43

This is just noting a trend, it is observation, not logic.

One very seldom states a material condition with false premises on purpose unless one is being facetious. All material conditionals with false premises are true, but have no useful consequences. So there is little motivation to actually say them.

One very seldom states a condition in the subjunctive with true premises about which one is certain on purpose. If it would be true in a given scenario, and this is that scenario, well then it is just confusing to bring up the idea there is a scenario involved at all. A subjunctive conditional with true premises just creates unnecessary mental work.

Good question! Nothing too deep here ... it's just that counterfactuals with true antecedents are rather boring. On most semantics, counterfactuals with true antecedents just collapse into material conditionals, so there's usually no point in writing them as counterfactuals. But you can write out any counterfactuals that you'd like if the fancy strikes you.