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Alex

Logical implication and evidence

From what I’ve read on Wikipedia, a valid logical implication is only when P is a sufficient condition for Q. So if something is a cat, it logically implies that it’s an animal. This also means that correlation does not imply causation since it’s not a sufficient condition for causation. So far so good.

 

But now here’s an issue. People don’t always use the word “imply” in that strict logical sense right? Let me try to elaborate things more. If I know that when my cat is outside it’s  usually  because my parents are inside the house, does this give me the right to claim that “my cat being outside implies  that my parents are inside”? If we analyze the problem, we can see that just because my cat is outside does not mean that my parents are inside, so it’s not a sufficient condition right. This is just a positive correlation.  Here’s my main question: can this be counted as “evidence” for my parents being inside even if it isn’t a sufficient condition? And does “evidence” HAVE to be accompanied by the strict logical implication I mentioned?

 

 

asked on Wednesday, Mar 30, 2022 10:15:27 AM by Alex

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Answers

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Ed F
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There are two main types of logic, deductive, and inductive.  In deductive logic, "P implies Q" means, as you said, that P is a sufficient condition for Q; if P is true then Q is true.   

In Inductive Logic, the premises do not "imply" in the strict sense that the conclusion is true; a strong inductive argument is one where if the premises are true, the conclusion is  probably true.

So this would be a strong inductive argument:

P1  When my cat is outside, it's usually because my parents are inside.

P2. My cat is outside.

C:  Therefore, probably my parents are inside.

Note that if you change " it's usually " in P1 to " it's always the case ", then the Conclusion will be "My parents are inside ( not just probably ), and it becomes a Deductive argument.

 

answered on Wednesday, Mar 30, 2022 10:32:42 AM by Ed F

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Alex writes:

So if someone is known to almost always say true things, and this person someday said that ghosts exist, does that imply that ghosts truly exist?

posted on Wednesday, Mar 30, 2022 10:46:44 AM
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Ed F writes:
[To Alex]

No, only if that someone  always (not almost always) says true things.  If that statement were used it'd be a deductive argument.  But unless one believes in an omniscient being, there is no such person.

[ login to reply ] posted on Wednesday, Mar 30, 2022 11:18:34 AM
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Alex writes:
[To Ed F]

Why does it have to be always? I’m talking about an inductive argument here.

 

Also I have another question that’s kinda irrelevant. I know I asked it so many times but I still don’t get it. If we have a LOT of weak inductive arguments, and let’s say each one of them has a probability of being true of about 0.05%, do we  add up  the probabilities to reach the total which may be like 50%? If not then what do we do? I’m still struggling a bit with Bayesian stuff.

[ login to reply ] posted on Wednesday, Mar 30, 2022 11:28:34 AM
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Ed F writes:
[To Alex]

If you’re talking about an Inductive Argument and the premise is that someone is known to “almost always” say true things, then it does not follow that anything they say is true  They almost always say true things; this may be one of the cases where they don’t.

As to your latter question, Weak Inductive Arguments are not cumulative; therefore the probabilities do not add up just by having a lot of weak arguments.   However, Evidence may be cumulative; the more evidence you get for a conclusion, the more probable the conclusion is and if you get enough evidence,  then at some point the evidence (premises) may pass the threshold and make the conclusion probable (and therefore become a strong argument).

[ login to reply ] posted on Wednesday, Mar 30, 2022 12:17:19 PM
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Alex writes:
[To Ed F]

Thanks for the new knowledge!

May I ask why exactly are weak inductive arguments considered to be not cumulative? Does it have something to do with math?

[ login to reply ] posted on Wednesday, Mar 30, 2022 03:58:25 PM
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Ed F writes:
[To Alex]

Arguments aren't the kind of thing you can add, or keep score on.   

By definition, a weak inductive argument doesn't prove its conclusion; that's why it's considered weak.  So coming up with additional weak inductive arguments doesn't add to the likelihood that the conclusion is true.

[ login to reply ] posted on Wednesday, Mar 30, 2022 04:24:38 PM