Oh alright, but it's not really as interesting as all that. False implications in the logical context are commonly referred to as logical fallacies. Wikipedia has a (non-exhaustive) list of those. One of the more famous false implications is interesting in that it maps between types of implication.
A is correlated with B implies that A implies (causal) B or B implies (causal) A (note that this is false, with a plethora of different types of counter example). This is probably the most commonly exploited false implication by hucksters, and, perhaps more importantly, is a very common source of false beliefs with no malicious intent at all.
It is easy to leverage this false belief into new false beliefs with true facts. If I want to sell coffee for example, I must convince someone of the buying coffee implies (causal) utility fact. All I must convince them of is that coffee is correlated with a thing that implies (causal) utility. Say for instance, that people with heart conditions have those conditions exacerbated negatively by taking coffee or drinking stimulants, and therefore don't. It follows then that drinking coffee is probably correlated with much better heart health. I phrase my findings as "People who drink coffee tend to have much better cardiac calcium scores", and just watch as people draw the incorrect conclusion about the utility of coffee from this fact, plus their fallacy (plus the additional assumption that better cardiac calcium scores probably don't cause coffee consumption).
I should note that It could very well be that coffee does have utility to you. So as a fact it might still be "true". So it turns out that what really ends up mattering, is not the facts, but the chains of implications that lead you to them.
Do you know if there is a way to encode these reasoning chains so as to assess their validity automatically? Like a knowledge graph with propositions linked in some way?
I have been reading about knowledge graphs but haven't seen this kind of application yet, but I think it should exist.
It depends on the (and I will use the term loosely here) "category" of interest. ie which kinds of implications you are talking about. Perhaps unsurprisingly, for mathematical propositions (constructive), these things do exist, and almost certainly surprisingly, they tend to be implemented as libraries of functions over a particular type system (constituting a less loose use of the word category).
For more statistical propositions, such as those that occur in science. Those exist but they're very flawed, and it's a tremendous effort to get anything useful out of them, on account of them dying when we try to look inside. If you haven't caught on, I'm talking about humans. We have yet to replicate such things automatically. You're certainly welcome to try though :).
Symbolic logic. Learn:
Truth tables -> rules of implication and replacement -> first order predicate logic -> quantifiers -> second order predicate logic.
Chapter 5 or 6 through 8 of Hurley's intro to logic does a great job imo.
> A is correlated with B implies that A implies (causal) B or B implies (causal) A (note that this is false, with a plethora of different types of counter example).
I think it's even worse:
implies:
- strongly suggest the truth or existence of (something not expressly stated)
- (of a fact or occurrence) suggest (something) as a logical consequence.
Unless your "implies (causal)" is a reference to a domain specific variation of the word (which laymen won't know anyways), your false conclusion is actually incorrect.
>> In casual use, the word "implies" loosely means suggests rather than requires. However, in logic, the technical use of the word "implies" means "is a sufficient condition for".[3] This is the meaning intended by statisticians when they say causation is not certain. Indeed, p implies q has the technical meaning of the material conditional: if p then q symbolized as p → q. That is "if circumstance p is true, then q follows." In this sense, it is always correct to say "Correlation does not imply causation."
> This is probably the most commonly exploited false implication by hucksters, and, perhaps more importantly, is a very common source of false beliefs with no malicious intent at all.
True, but then it's extremely easy to find large quantities of people on the internet who speak as if (I infer this from the surrounding text of their statement) correlation rules out the possibility of causation.
I would love to know the magnitude of confusion/harm the (typically unrealized) ambiguity and other issues of the English language causes in the world, especially considering how causality links so many things together (often in ways beyond our awareness).
Oh alright, but it's not really as interesting as all that. False implications in the logical context are commonly referred to as logical fallacies. Wikipedia has a (non-exhaustive) list of those. One of the more famous false implications is interesting in that it maps between types of implication.
A is correlated with B implies that A implies (causal) B or B implies (causal) A (note that this is false, with a plethora of different types of counter example). This is probably the most commonly exploited false implication by hucksters, and, perhaps more importantly, is a very common source of false beliefs with no malicious intent at all.
It is easy to leverage this false belief into new false beliefs with true facts. If I want to sell coffee for example, I must convince someone of the buying coffee implies (causal) utility fact. All I must convince them of is that coffee is correlated with a thing that implies (causal) utility. Say for instance, that people with heart conditions have those conditions exacerbated negatively by taking coffee or drinking stimulants, and therefore don't. It follows then that drinking coffee is probably correlated with much better heart health. I phrase my findings as "People who drink coffee tend to have much better cardiac calcium scores", and just watch as people draw the incorrect conclusion about the utility of coffee from this fact, plus their fallacy (plus the additional assumption that better cardiac calcium scores probably don't cause coffee consumption).
I should note that It could very well be that coffee does have utility to you. So as a fact it might still be "true". So it turns out that what really ends up mattering, is not the facts, but the chains of implications that lead you to them.