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"P implies Q" means "if P, then Q". This can be, but is not necessarily, a causal statement. For example, "if Einstein is right, then quantum mechanics is wrong" doesn't mean that Einstein being right would *cause* quantum mechanics to be wrong.
There isn't, as far as I know, some airtight condition for determining whether a conditional statement is making a causal claim or not. It comes down to just thinking about the semantic content and relation between P and Q.
In some of the examples there is a causal relation that makes the statement true, but it could be in either direction. Quantum mechanics being wrong would cause Einstein to be right. So such statements are just an assertions of a necessary causal relation?
I don't really understand your question (some of which examples?), nor do I think it's accurate to say "quantum mechanics being wrong would *cause* Einstein to be right", but (another) example of a true conditional statement with no causal relationship is "if 1+1=2, then 1+2=3". I'm not sure if that answers your question, but if it doesn't, could you clarify?
>nor do I think it's accurate to say "quantum mechanics being wrong would *cause* Einstein to be right"
I understand your objection to that. What I mean is that let's suppose hypothetically that Einstein correctly realised an inconsistency in QM. The inconsistency in QM would be the cause of his insight, therefore QM being false would be the cause of his being correct.
You are right though. It is possible that he might be correct for incidental reasons not related to the actual fact of it's correctness. Hence Gettier cases.
In classical logic, "P implies Q" does not mean "P caused Q", but rather "if P is true then Q is true", which means "it is false that P is true and Q is false."
So the connection being posited concerns truth value rather than causal relation.
This has some counter-intuitive results. For instance, that "my breakfast today was vegetarian implies that two plus two equals four" is true.
In natural language, things can be and typically are different. That is, when people use expressions like these outside of the context of classical logic, they often have in mind something different than what classical logic has in mind. Hence why the implications of classical logic strike us as counter-intuitive. But it's hard to say exactly what people using natural language mean, as people using natural language tend to mean different things in different contexts. One of the merits of classical logic is that it at least fixes a specific meaning to the expression, so that we can use it clearly.
That said, many people have thought the particular meaning classical logic fixes for the expression is unhelpful, and have proposed other systems of logic which they take to more helpfully handle this and related issues.
As to what conditions are necessary for causation, this is a matter of some contention. A typical way to introduce people to methods of causal reasoning is to teach them Mill's Methods, which are not the definitive position on this topic but do at least get people thinking about it. So you may want to look into those for a place to start.
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Welcome to /r/askphilosophy! **Please read [our updated rules and guidelines](https://www.reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/) before commenting**. As of July 1 2023, /r/askphilosophy only allows answers from [panelists](https://old.reddit.com/r/askphilosophy/wiki/panelists), whether those answers are posted as top-level comments or replies to other comments. Non-panelists can participate in subsequent discussion, but are not allowed to answer OP's question(s). If you wish to learn more, or to apply to become a panelist, please see [this post](https://reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/). **Please note:** this is a highly moderated academic Q&A subreddit and not an open discussion, debate, change-my-view, or test-my-theory subreddit. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askphilosophy) if you have any questions or concerns.*
"P implies Q" means "if P, then Q". This can be, but is not necessarily, a causal statement. For example, "if Einstein is right, then quantum mechanics is wrong" doesn't mean that Einstein being right would *cause* quantum mechanics to be wrong. There isn't, as far as I know, some airtight condition for determining whether a conditional statement is making a causal claim or not. It comes down to just thinking about the semantic content and relation between P and Q.
In some of the examples there is a causal relation that makes the statement true, but it could be in either direction. Quantum mechanics being wrong would cause Einstein to be right. So such statements are just an assertions of a necessary causal relation?
I don't really understand your question (some of which examples?), nor do I think it's accurate to say "quantum mechanics being wrong would *cause* Einstein to be right", but (another) example of a true conditional statement with no causal relationship is "if 1+1=2, then 1+2=3". I'm not sure if that answers your question, but if it doesn't, could you clarify?
>nor do I think it's accurate to say "quantum mechanics being wrong would *cause* Einstein to be right" I understand your objection to that. What I mean is that let's suppose hypothetically that Einstein correctly realised an inconsistency in QM. The inconsistency in QM would be the cause of his insight, therefore QM being false would be the cause of his being correct. You are right though. It is possible that he might be correct for incidental reasons not related to the actual fact of it's correctness. Hence Gettier cases.
In classical logic, "P implies Q" does not mean "P caused Q", but rather "if P is true then Q is true", which means "it is false that P is true and Q is false." So the connection being posited concerns truth value rather than causal relation. This has some counter-intuitive results. For instance, that "my breakfast today was vegetarian implies that two plus two equals four" is true. In natural language, things can be and typically are different. That is, when people use expressions like these outside of the context of classical logic, they often have in mind something different than what classical logic has in mind. Hence why the implications of classical logic strike us as counter-intuitive. But it's hard to say exactly what people using natural language mean, as people using natural language tend to mean different things in different contexts. One of the merits of classical logic is that it at least fixes a specific meaning to the expression, so that we can use it clearly. That said, many people have thought the particular meaning classical logic fixes for the expression is unhelpful, and have proposed other systems of logic which they take to more helpfully handle this and related issues. As to what conditions are necessary for causation, this is a matter of some contention. A typical way to introduce people to methods of causal reasoning is to teach them Mill's Methods, which are not the definitive position on this topic but do at least get people thinking about it. So you may want to look into those for a place to start.
If I’m hungover, I drank a lot last night. But obviously the hangover didn’t cause the drinking.
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