>> The conjunction of two events can’t be more likely than just one event by itself.

> This is mathematically incorrect. If two events are mutually dependent on the other to occur then two events are more likely to occur together than either or independently.

The original statement is correct. You are talking about conditional probability: the probability that one event will occur given that another event has occurred. i.e. if A and B are two events P(A|B), read as the probability of A given B. This is equal to P(A and B)/P(B). Notice that, The conjunction of the two events, P(A and B), is divided by the probability of B, P(B). We have reduced the probability space to the smaller space of just B. The conjunction of two events is just their set intersection (at least in a probability system which defines events as sets of outcomes) and can never be larger than either event.

Calculating the probability that A and a sequential event B will happen rather than inferring the probability of A given an a posteriori event B might be more intuitive to bring up in this argument.

An easy way to explain how the conclusion was derived is just by considering that we have to multiply probabilities to calculate the probability of a conjunction of events, and since most probabilities are below 1, the number will always be less than or equal to a single event.

This doesn't take people being able to choose how to think into account.

The logic is sound so I'm not sure how "being able to choose how to think" changes anything

Go back to the original article. Now think about it being used to disprove everything you think about things instead of it being used to prove everything you think about things.

That assumes events are sequentially occurring.

I think there's an issue of terminology.

Please see https://en.wikipedia.org/wiki/Event_(probability_theory) and https://en.wikipedia.org/wiki/Probability_space for what mathematical statistics means by the term "event".

I suspect that what you are calling "events" are actually values of some function defined on the set of (mathematical) events. Such a function is called a random variable. The values of a random variable are a major object of study in statistics - but they are not events.

I'm trying to direct this conversation away from using logic and math to reason about interpersonal relationships. It's garbage. Math talks about math. Logic talks about logic. This article conflates it with how people think about one another.

They are calling an event that occurs twice a singular event. My mind, your mind, the same statement, understood and accepted twice, possibly at different points in time (which is obvious given the fact that I have to literally hit send on this message) but you may be thinking the same thoughts as I at the same time, mutually dependent because we are all idiots that think it's fine to use logic and math to describe all minds.

It's not an RV when it comes to thoughts you choose to think! The RV is the thoughts you don't want to think.

The origin mask quote(“The conjunction of two events can’t be more likely than just one event by itself.”) was in the context of an experiment in which subjects were given a description of a person and they responded that it was more likely she was a “feminist bank-teller” than either just a feminist or just a bank-teller. Here the appeal to formal probability is justified because obviously there are more bank-tellers than feminist bank-tellers, and likewise more feminists than feminist bank tellers.

That's not the point of the article. The greater context is about the relation between an individual mind and other minds.

Paraconsistent logic allows contradicting statements to be held without implying one must be true or the other.

Why would there obviously be more feminist bank tellers than female bank tellers? What if there's a cultural connection that guides both decisions to be made together?

Don't people aggregate personality details in clusters by choice in order to be accepted via conformity? Isn't that the principle recommendation engines operate on fundamentally?

> Why would there obviously be more feminist bank tellers than female bank tellers?

No! You still aren't paying attention and at this point I think you might be just trolling, but here's one more good faith response.

To reiterate, the article brings up the interesting result that people think it's more likely that someone is a "feminist bank teller" than that she is a "bank teller".

To be clear there are some number of bank tellers, and of them, some are feminist. There cannot be more people who are feminist and bank tellers than people who are simply bank tellers. The feminist ones are a subset of all bank tellers.

So the probability that someone is both is less than or equal to the probability that someone is just a bank teller. If you know them well, and they go to marches and such and your ascertain that they are definitely feminist, then the probability that they are both is equal to (but not greater) than the probability that they're a bank teller.

You are right for the tiny very specific example they are using.

Honestly if I try to explain my reasoning, it's just a waste of energy at this point. Behavior, people, you can't predict it. You can't predict thoughts people have. Can't infer intent for why people use one pedantic example to illustrate a point over another.

>This doesn't give people the chance to change if the whole system is based on everyone retaining an internal consistency in inferencing that is checked against reality by testing it.

Yes it does, start being honest and eventually people's most recent memories or interactions with you will be ones of honesty. This is different, of course, than the one strike and your out criminal offense system in the U.S.

I'm speaking hypothetically, first.

Secondly, that assumes way too much about how people think.

> If two events are mutually dependent on the other to occur then two events are more likely to occur together than either or independently.

But that's not the statement that you're saying is incorrect. In your scenario, if A and B always occur together then P(A) == P(B) == P(A & B), and the original statement that P(A & B) is not greater than either P(A) or P(B) is still true (it's equal).

The reasoning they are using isn't pure logic or math. You need more than logic and math to reason about people emotionally.

There's mutually established dependencies in relationships. One depends on the other but both minds think.

This is ridiculous reasoning to turn this crap into a math or logical expression to begin with. The fact that we have to argue out of common sense about emotions with logic and math is ridiculous enough and sucks because guess what! We know we reasoned ourselves into it.

People affect one another. Sometimes people understand each other mutually at the same time. It's not out of the space of probability for empathy to happen at the same moment in time and be dependent on the fact that both people are working towards it together.

The statement is that P(A ∧ B) is always less than or equal to both P(A) and P(B). You're arguing that P(A ∧ B) can be greater than P(A ∧ ¬B) and can be greater than P(B ∧ ¬A), which is true, but it's a totally different statement. You're confused about the language, and building some emotions-based interpretation around it.

> You're confused about the language, and building some emotions-based interpretation around it.

That is what the article is about.

I believe there are more ways to reason than just using logic or probability when it comes to determining how people think. That's just reality. The crux of my argument rests on thinking about thinking.

Also, please don't tell me I'm confused. I'm not confused. You are cherry picking an argument and that has derailed me from my original point. Thinking about thinking influences the probabilities of what thoughts will occur as consequence in ways that are intrinsically entangled. You can extrapolate that reasoning to yield how and why people think about how other people think and for what purpose.

Please reread what I said originally instead of latching on a single point by taking advantage of the fact that multiple people have responded to different points in unison to my perspective. You know I can assume you are responding to a specific point and you can continue directing the conversation using that point to begin with as a foundation for weakening my argument. You also know I can't assume you have read the whole lineage of comments resulting from my original argument, as can anyone else responding to this thread chain.

I said mutually dependent - you can try to understand this if you choose to do so. But honestly all of this is ridiculous.

Edit: internal inconsistency is just as adequate